Comprehension
Answer the questions based on the information given below.
Five persons – Prakash, Ritik, Sahil, Tushar and Dheeraj have some notes in denomination of Rs. 20, Rs. 50 and Rs. 100 but it is not necessary that person certainly has notes of all the given three denominations with them. The ratio of total amount with Sahil and Tushar is 2:3, respectively. Total amount with Tushar is 12.5% more than that with Prakash. Total amount with Ritik is Rs. 170 less than that with Prakash and Rs. 350 less than that with Dheeraj. Dheeraj has a total of Rs. 580 with him.
Additional information:
1.) Total number of notes with Prakash is more than 10 but less than 13 and Prakash has only Rs. 20 and Rs. 50 notes. The number of Rs. 50 notes with Prakash is more than the number of Rs. 20 notes.
2.) Ritik has only Rs. 20 and Rs. 50 notes and the number of Rs. 20 notes with him is more than number of Rs. 50 notes with him.
3.) Sahil has the notes of Rs. 20 and Rs. 100 denominations only.
4.) Tushar has only Rs. 50 and Rs. 100 notes and the number of notes that Sahil has is same as the number of notes that Tushar has.
5.) Dheeraj has the notes of all three denominations and the number of Rs. 20 notes that Ritik has is same as the number of Rs. 20 notes that Dheeraj has. Total number of notes that Prakash has is same as total number of notes that Dheeraj has.
Five persons – Prakash, Ritik, Sahil, Tushar and Dheeraj have some notes in denomination of Rs. 20, Rs. 50 and Rs. 100 but it is not necessary that person certainly has notes of all the given three denominations with them. The ratio of total amount with Sahil and Tushar is 2:3, respectively. Total amount with Tushar is 12.5% more than that with Prakash. Total amount with Ritik is Rs. 170 less than that with Prakash and Rs. 350 less than that with Dheeraj. Dheeraj has a total of Rs. 580 with him.
Additional information:
1.) Total number of notes with Prakash is more than 10 but less than 13 and Prakash has only Rs. 20 and Rs. 50 notes. The number of Rs. 50 notes with Prakash is more than the number of Rs. 20 notes.
2.) Ritik has only Rs. 20 and Rs. 50 notes and the number of Rs. 20 notes with him is more than number of Rs. 50 notes with him.
3.) Sahil has the notes of Rs. 20 and Rs. 100 denominations only.
4.) Tushar has only Rs. 50 and Rs. 100 notes and the number of notes that Sahil has is same as the number of notes that Tushar has.
5.) Dheeraj has the notes of all three denominations and the number of Rs. 20 notes that Ritik has is same as the number of Rs. 20 notes that Dheeraj has. Total number of notes that Prakash has is same as total number of notes that Dheeraj has.
Question: 1
Find the total number of notes that Ritik has?
Find the total number of notes that Ritik has?
Updated On: Aug 31, 2024
- 11
- 10
- 5
- 7
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The Correct Option is D
Solution and Explanation
Total amount with Dheeraj = Rs. 580
Total amount with Ritik = 580 – 350 = Rs. 230
Total amount with Prakash = 230 + 170 = Rs. 400
Total amount with Tushar = 1.125 × 400 = Rs. 450
Total amount with Sahil = 450 × (2/3) = Rs. 300
For Prakash:
Prakash has Rs. 400 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 400 – 100 = 300
So, the number of Rs. 50 denomination notes = \(\frac{300}{50}\)= 6
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 400 – 200 = 200
So, the number of Rs. 50 denomination notes = \(\frac{200}{50}\)= 4
But, the number of Rs. 50 notes with Prakash is more than the number of
Rs. 20 notes. So, case 2 is eliminated.
The number of notes of Rs. 20 and Rs. 50 denomination with Prakash is ‘5’ and ‘6’, respectively.
For Ritik:
Ritik has Rs. 230 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 1 × 50 = Rs. 50
Remaining amount = 230 – 50 = 180
So, the number of Rs. 20 denomination notes = 180/20 = 9
Case 2:
Let the number of Rs. 50 denomination notes = 2
So, the value of Rs. 50 denomination notes = 2 × 50 = Rs. 100
Remaining amount = 230 – 100 = 130
So, the number of Rs. 20 denomination notes = \(\frac{130}{2}\)= 6.5
This case is not possible.
Case 3:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 3 × 50 = Rs. 150
Remaining amount = 230 – 150 = 80
So, the number of Rs. 20 denomination notes = \(\frac{80}{20}\) = 4
Case 4:
Let the number of Rs. 50 denomination notes = 4
So, the value of Rs. 50 denomination notes = 4 × 50 = Rs. 200
Remaining amount = 230 – 200 = 30
So, the number of Rs. 20 denomination notes = \(\frac{30}{20}\) = 1.5
This case is not possible.
Case 5:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 5 × 50 = Rs. 250
This case is not possible.
For Sahil:
Sahil has Rs. 300 with him in the denominations of Rs. 20 and Rs. 100 only.
Since, amount corresponding to Rs. 100 notes will be in multiple of 100 only.
Therefore, number of notes of Rs. 20 should in multiple of 100 so that
total amount will also be in multiple on 100.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 300 – 100 = 200
So, the number of Rs. 100 denomination notes = \(\frac{200}{100}\) = 2
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 300 – 200 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
For Tushar:
Tushar has Rs. 450 with him in the denominations of Rs. 50 and Rs. 100 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 50 × 1 = Rs. 50
Remaining amount = 450 – 50 = 400
So, the number of Rs. 100 denomination notes = \(\frac{400}{100}\)= 4
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 2:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 50 × 3 = Rs. 150
Remaining amount = 450 – 150 = 300
So, the number of Rs. 100 denomination notes =\(\frac{300}{100}\)= 3
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 3:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 50 × 5 = Rs. 250
Remaining amount = 450 – 250 = 200
So, the number of Rs. 100 denomination notes =\(\frac{200}{100}\)= 2
This case is possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 4:
Let the number of Rs. 50 denomination notes = 7
So, the value of Rs. 50 denomination notes = 50 × 7 = Rs. 350
Remaining amount = 450 – 350 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Only possible case for Tushar:
The number of Rs. 50 denomination notes = 5
The number of Rs. 100 denomination notes = 2
Only possible case for Sahil:
The number of Rs. 20 denomination notes = 5
The number of Rs. 100 denomination notes = 2
For Dheeraj:
Dheeraj has Rs. 580 with him in the denominations of Rs. 20, Rs. 50 and Rs. 100 only.
The number of Rs. 20 denomination notes = 4 or 9
The total number of notes that Dheeraj has = 11
Case 1:
The number of Rs. 20 denomination notes = 4
So, the value of Rs. 20 denomination notes = 20 × 4 = Rs. 80
Remaining amount = 580 – 80 = 500
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 4 = 7
If the number of notes of Rs. 50 denomination will be 2 then the number of notes of Rs. 100 denomination will be 5. But this is not possible,
because then the total value of Rs. 50 and Rs. 100 notes together will be
Rs. 600.
If the number of notes of Rs. 50 denomination is 4, then the number of
notes of Rs. 100 denomination will be 3. And this is possible, because, the total value of Rs. 50 and Rs. 100 notes together will be Rs. 500.
If the number of notes of Rs. 50 denomination is 6, then the number of
notes of Rs. 100 denomination will be 1. And this is not possible, because,
the total value of Rs. 50 and Rs. 100 notes together will be Rs. 400.
Case 2:
The number of Rs. 20 denomination notes = 9
So, the value of Rs. 20 denomination notes = 20 × 9 = Rs. 180
Remaining amount = 580 – 180 = 400
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 9 = 2
The number of notes of Rs. 50 and Rs. 100 denomination is 1 each.
But this is not possible, because the total value of Rs. 50 and Rs. 100 notes together l be Rs. 150.
So, the number of Rs. 20 and Rs. 50 denomination notes with Ritik is 4 and 3, respectively.
And, the number of Rs. 20, Rs. 50 and Rs. 100 denomination notes of
Dheeraj is 4, 4 and 3, respectively.
Total number of notes that Ritik has = 4 + 3 = 7
So, the correct option is (D): 7.
Total amount with Ritik = 580 – 350 = Rs. 230
Total amount with Prakash = 230 + 170 = Rs. 400
Total amount with Tushar = 1.125 × 400 = Rs. 450
Total amount with Sahil = 450 × (2/3) = Rs. 300
For Prakash:
Prakash has Rs. 400 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 400 – 100 = 300
So, the number of Rs. 50 denomination notes = \(\frac{300}{50}\)= 6
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 400 – 200 = 200
So, the number of Rs. 50 denomination notes = \(\frac{200}{50}\)= 4
But, the number of Rs. 50 notes with Prakash is more than the number of
Rs. 20 notes. So, case 2 is eliminated.
The number of notes of Rs. 20 and Rs. 50 denomination with Prakash is ‘5’ and ‘6’, respectively.
For Ritik:
Ritik has Rs. 230 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 1 × 50 = Rs. 50
Remaining amount = 230 – 50 = 180
So, the number of Rs. 20 denomination notes = 180/20 = 9
Case 2:
Let the number of Rs. 50 denomination notes = 2
So, the value of Rs. 50 denomination notes = 2 × 50 = Rs. 100
Remaining amount = 230 – 100 = 130
So, the number of Rs. 20 denomination notes = \(\frac{130}{2}\)= 6.5
This case is not possible.
Case 3:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 3 × 50 = Rs. 150
Remaining amount = 230 – 150 = 80
So, the number of Rs. 20 denomination notes = \(\frac{80}{20}\) = 4
Case 4:
Let the number of Rs. 50 denomination notes = 4
So, the value of Rs. 50 denomination notes = 4 × 50 = Rs. 200
Remaining amount = 230 – 200 = 30
So, the number of Rs. 20 denomination notes = \(\frac{30}{20}\) = 1.5
This case is not possible.
Case 5:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 5 × 50 = Rs. 250
This case is not possible.
For Sahil:
Sahil has Rs. 300 with him in the denominations of Rs. 20 and Rs. 100 only.
Since, amount corresponding to Rs. 100 notes will be in multiple of 100 only.
Therefore, number of notes of Rs. 20 should in multiple of 100 so that
total amount will also be in multiple on 100.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 300 – 100 = 200
So, the number of Rs. 100 denomination notes = \(\frac{200}{100}\) = 2
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 300 – 200 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
For Tushar:
Tushar has Rs. 450 with him in the denominations of Rs. 50 and Rs. 100 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 50 × 1 = Rs. 50
Remaining amount = 450 – 50 = 400
So, the number of Rs. 100 denomination notes = \(\frac{400}{100}\)= 4
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 2:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 50 × 3 = Rs. 150
Remaining amount = 450 – 150 = 300
So, the number of Rs. 100 denomination notes =\(\frac{300}{100}\)= 3
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 3:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 50 × 5 = Rs. 250
Remaining amount = 450 – 250 = 200
So, the number of Rs. 100 denomination notes =\(\frac{200}{100}\)= 2
This case is possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 4:
Let the number of Rs. 50 denomination notes = 7
So, the value of Rs. 50 denomination notes = 50 × 7 = Rs. 350
Remaining amount = 450 – 350 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Only possible case for Tushar:
The number of Rs. 50 denomination notes = 5
The number of Rs. 100 denomination notes = 2
Only possible case for Sahil:
The number of Rs. 20 denomination notes = 5
The number of Rs. 100 denomination notes = 2
For Dheeraj:
Dheeraj has Rs. 580 with him in the denominations of Rs. 20, Rs. 50 and Rs. 100 only.
The number of Rs. 20 denomination notes = 4 or 9
The total number of notes that Dheeraj has = 11
Case 1:
The number of Rs. 20 denomination notes = 4
So, the value of Rs. 20 denomination notes = 20 × 4 = Rs. 80
Remaining amount = 580 – 80 = 500
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 4 = 7
If the number of notes of Rs. 50 denomination will be 2 then the number of notes of Rs. 100 denomination will be 5. But this is not possible,
because then the total value of Rs. 50 and Rs. 100 notes together will be
Rs. 600.
If the number of notes of Rs. 50 denomination is 4, then the number of
notes of Rs. 100 denomination will be 3. And this is possible, because, the total value of Rs. 50 and Rs. 100 notes together will be Rs. 500.
If the number of notes of Rs. 50 denomination is 6, then the number of
notes of Rs. 100 denomination will be 1. And this is not possible, because,
the total value of Rs. 50 and Rs. 100 notes together will be Rs. 400.
Case 2:
The number of Rs. 20 denomination notes = 9
So, the value of Rs. 20 denomination notes = 20 × 9 = Rs. 180
Remaining amount = 580 – 180 = 400
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 9 = 2
The number of notes of Rs. 50 and Rs. 100 denomination is 1 each.
But this is not possible, because the total value of Rs. 50 and Rs. 100 notes together l be Rs. 150.
So, the number of Rs. 20 and Rs. 50 denomination notes with Ritik is 4 and 3, respectively.
And, the number of Rs. 20, Rs. 50 and Rs. 100 denomination notes of
Dheeraj is 4, 4 and 3, respectively.
| Persons | Number of notes of | ||
| Rs. 20 | Rs. 50 | Rs. 100 | |
| Prakash | 5 | 6 | - |
| Ritik | 4 | 3 | - |
| Sahil | 5 | - | 2 |
| Tushar | - | 5 | 2 |
| Dheeraj | 4 | 4 | 3 |
So, the correct option is (D): 7.
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Question: 2
What is the total value of all the Rs. 20 denomination notes that Sahil has?
What is the total value of all the Rs. 20 denomination notes that Sahil has?
Updated On: Aug 31, 2024
- Rs.120
- Rs.1601
- Rs.200
- Rs.100
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The Correct Option is D
Solution and Explanation
Total amount with Dheeraj = Rs. 580
Total amount with Ritik = 580 – 350 = Rs. 230
Total amount with Prakash = 230 + 170 = Rs. 400
Total amount with Tushar = 1.125 × 400 = Rs. 450
Total amount with Sahil = 450 × (2/3) = Rs. 300
For Prakash:
Prakash has Rs. 400 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 400 – 100 = 300
So, the number of Rs. 50 denomination notes = \(\frac{300}{50}\)= 6
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 400 – 200 = 200
So, the number of Rs. 50 denomination notes = \(\frac{200}{50}\)= 4
But, the number of Rs. 50 notes with Prakash is more than the number of
Rs. 20 notes. So, case 2 is eliminated.
The number of notes of Rs. 20 and Rs. 50 denomination with Prakash is ‘5’ and ‘6’, respectively.
For Ritik:
Ritik has Rs. 230 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 1 × 50 = Rs. 50
Remaining amount = 230 – 50 = 180
So, the number of Rs. 20 denomination notes = 180/20 = 9
Case 2:
Let the number of Rs. 50 denomination notes = 2
So, the value of Rs. 50 denomination notes = 2 × 50 = Rs. 100
Remaining amount = 230 – 100 = 130
So, the number of Rs. 20 denomination notes = \(\frac{130}{2}\)= 6.5
This case is not possible.
Case 3:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 3 × 50 = Rs. 150
Remaining amount = 230 – 150 = 80
So, the number of Rs. 20 denomination notes = \(\frac{80}{20}\) = 4
Case 4:
Let the number of Rs. 50 denomination notes = 4
So, the value of Rs. 50 denomination notes = 4 × 50 = Rs. 200
Remaining amount = 230 – 200 = 30
So, the number of Rs. 20 denomination notes = \(\frac{30}{20}\) = 1.5
This case is not possible.
Case 5:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 5 × 50 = Rs. 250
This case is not possible.
For Sahil:
Sahil has Rs. 300 with him in the denominations of Rs. 20 and Rs. 100 only.
Since, amount corresponding to Rs. 100 notes will be in multiple of 100 only.
Therefore, number of notes of Rs. 20 should in multiple of 100 so that
total amount will also be in multiple on 100.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 300 – 100 = 200
So, the number of Rs. 100 denomination notes = \(\frac{200}{100}\) = 2
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 300 – 200 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
For Tushar:
Tushar has Rs. 450 with him in the denominations of Rs. 50 and Rs. 100 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 50 × 1 = Rs. 50
Remaining amount = 450 – 50 = 400
So, the number of Rs. 100 denomination notes = \(\frac{400}{100}\)= 4
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 2:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 50 × 3 = Rs. 150
Remaining amount = 450 – 150 = 300
So, the number of Rs. 100 denomination notes =\(\frac{300}{100}\)= 3
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 3:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 50 × 5 = Rs. 250
Remaining amount = 450 – 250 = 200
So, the number of Rs. 100 denomination notes =\(\frac{200}{100}\)= 2
This case is possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 4:
Let the number of Rs. 50 denomination notes = 7
So, the value of Rs. 50 denomination notes = 50 × 7 = Rs. 350
Remaining amount = 450 – 350 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Only possible case for Tushar:
The number of Rs. 50 denomination notes = 5
The number of Rs. 100 denomination notes = 2
Only possible case for Sahil:
The number of Rs. 20 denomination notes = 5
The number of Rs. 100 denomination notes = 2
For Dheeraj:
Dheeraj has Rs. 580 with him in the denominations of Rs. 20, Rs. 50 and Rs. 100 only.
The number of Rs. 20 denomination notes = 4 or 9
The total number of notes that Dheeraj has = 11
Case 1:
The number of Rs. 20 denomination notes = 4
So, the value of Rs. 20 denomination notes = 20 × 4 = Rs. 80
Remaining amount = 580 – 80 = 500
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 4 = 7
If the number of notes of Rs. 50 denomination will be 2 then the number of notes of Rs. 100 denomination will be 5. But this is not possible,
because then the total value of Rs. 50 and Rs. 100 notes together will be
Rs. 600.
If the number of notes of Rs. 50 denomination is 4, then the number of
notes of Rs. 100 denomination will be 3. And this is possible, because, the total value of Rs. 50 and Rs. 100 notes together will be Rs. 500.
If the number of notes of Rs. 50 denomination is 6, then the number of
notes of Rs. 100 denomination will be 1. And this is not possible, because,
the total value of Rs. 50 and Rs. 100 notes together will be Rs. 400.
Case 2:
The number of Rs. 20 denomination notes = 9
So, the value of Rs. 20 denomination notes = 20 × 9 = Rs. 180
Remaining amount = 580 – 180 = 400
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 9 = 2
The number of notes of Rs. 50 and Rs. 100 denomination is 1 each.
But this is not possible, because the total value of Rs. 50 and Rs. 100 notes together l be Rs. 150.
So, the number of Rs. 20 and Rs. 50 denomination notes with Ritik is 4 and 3, respectively.
And, the number of Rs. 20, Rs. 50 and Rs. 100 denomination notes of
Dheeraj is 4, 4 and 3, respectively.
Total value of all the Rs. 20 denomination notes that Sahil has = 20 × 5 = Rs. 100
So, the correct option is (D): 100.
Total amount with Ritik = 580 – 350 = Rs. 230
Total amount with Prakash = 230 + 170 = Rs. 400
Total amount with Tushar = 1.125 × 400 = Rs. 450
Total amount with Sahil = 450 × (2/3) = Rs. 300
For Prakash:
Prakash has Rs. 400 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 400 – 100 = 300
So, the number of Rs. 50 denomination notes = \(\frac{300}{50}\)= 6
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 400 – 200 = 200
So, the number of Rs. 50 denomination notes = \(\frac{200}{50}\)= 4
But, the number of Rs. 50 notes with Prakash is more than the number of
Rs. 20 notes. So, case 2 is eliminated.
The number of notes of Rs. 20 and Rs. 50 denomination with Prakash is ‘5’ and ‘6’, respectively.
For Ritik:
Ritik has Rs. 230 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 1 × 50 = Rs. 50
Remaining amount = 230 – 50 = 180
So, the number of Rs. 20 denomination notes = 180/20 = 9
Case 2:
Let the number of Rs. 50 denomination notes = 2
So, the value of Rs. 50 denomination notes = 2 × 50 = Rs. 100
Remaining amount = 230 – 100 = 130
So, the number of Rs. 20 denomination notes = \(\frac{130}{2}\)= 6.5
This case is not possible.
Case 3:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 3 × 50 = Rs. 150
Remaining amount = 230 – 150 = 80
So, the number of Rs. 20 denomination notes = \(\frac{80}{20}\) = 4
Case 4:
Let the number of Rs. 50 denomination notes = 4
So, the value of Rs. 50 denomination notes = 4 × 50 = Rs. 200
Remaining amount = 230 – 200 = 30
So, the number of Rs. 20 denomination notes = \(\frac{30}{20}\) = 1.5
This case is not possible.
Case 5:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 5 × 50 = Rs. 250
This case is not possible.
For Sahil:
Sahil has Rs. 300 with him in the denominations of Rs. 20 and Rs. 100 only.
Since, amount corresponding to Rs. 100 notes will be in multiple of 100 only.
Therefore, number of notes of Rs. 20 should in multiple of 100 so that
total amount will also be in multiple on 100.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 300 – 100 = 200
So, the number of Rs. 100 denomination notes = \(\frac{200}{100}\) = 2
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 300 – 200 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
For Tushar:
Tushar has Rs. 450 with him in the denominations of Rs. 50 and Rs. 100 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 50 × 1 = Rs. 50
Remaining amount = 450 – 50 = 400
So, the number of Rs. 100 denomination notes = \(\frac{400}{100}\)= 4
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 2:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 50 × 3 = Rs. 150
Remaining amount = 450 – 150 = 300
So, the number of Rs. 100 denomination notes =\(\frac{300}{100}\)= 3
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 3:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 50 × 5 = Rs. 250
Remaining amount = 450 – 250 = 200
So, the number of Rs. 100 denomination notes =\(\frac{200}{100}\)= 2
This case is possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 4:
Let the number of Rs. 50 denomination notes = 7
So, the value of Rs. 50 denomination notes = 50 × 7 = Rs. 350
Remaining amount = 450 – 350 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Only possible case for Tushar:
The number of Rs. 50 denomination notes = 5
The number of Rs. 100 denomination notes = 2
Only possible case for Sahil:
The number of Rs. 20 denomination notes = 5
The number of Rs. 100 denomination notes = 2
For Dheeraj:
Dheeraj has Rs. 580 with him in the denominations of Rs. 20, Rs. 50 and Rs. 100 only.
The number of Rs. 20 denomination notes = 4 or 9
The total number of notes that Dheeraj has = 11
Case 1:
The number of Rs. 20 denomination notes = 4
So, the value of Rs. 20 denomination notes = 20 × 4 = Rs. 80
Remaining amount = 580 – 80 = 500
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 4 = 7
If the number of notes of Rs. 50 denomination will be 2 then the number of notes of Rs. 100 denomination will be 5. But this is not possible,
because then the total value of Rs. 50 and Rs. 100 notes together will be
Rs. 600.
If the number of notes of Rs. 50 denomination is 4, then the number of
notes of Rs. 100 denomination will be 3. And this is possible, because, the total value of Rs. 50 and Rs. 100 notes together will be Rs. 500.
If the number of notes of Rs. 50 denomination is 6, then the number of
notes of Rs. 100 denomination will be 1. And this is not possible, because,
the total value of Rs. 50 and Rs. 100 notes together will be Rs. 400.
Case 2:
The number of Rs. 20 denomination notes = 9
So, the value of Rs. 20 denomination notes = 20 × 9 = Rs. 180
Remaining amount = 580 – 180 = 400
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 9 = 2
The number of notes of Rs. 50 and Rs. 100 denomination is 1 each.
But this is not possible, because the total value of Rs. 50 and Rs. 100 notes together l be Rs. 150.
So, the number of Rs. 20 and Rs. 50 denomination notes with Ritik is 4 and 3, respectively.
And, the number of Rs. 20, Rs. 50 and Rs. 100 denomination notes of
Dheeraj is 4, 4 and 3, respectively.
| Persons | Number of notes of | ||
| Rs. 20 | Rs. 50 | Rs. 100 | |
| Prakash | 5 | 6 | - |
| Ritik | 4 | 3 | - |
| Sahil | 5 | - | 2 |
| Tushar | - | 5 | 2 |
| Dheeraj | 4 | 4 | 3 |
So, the correct option is (D): 100.
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Question: 3
Which of the following statement(s) is/are definitely true?
I. Number of Rs. 50 notes that Ritik has is ‘3’.
II. Number of Rs. 20 notes that Dheeraj has is ‘9’.
III. Total value of Rs. 50 notes that Tushar has is Rs. 250.
Which of the following statement(s) is/are definitely true?
I. Number of Rs. 50 notes that Ritik has is ‘3’.
II. Number of Rs. 20 notes that Dheeraj has is ‘9’.
III. Total value of Rs. 50 notes that Tushar has is Rs. 250.
I. Number of Rs. 50 notes that Ritik has is ‘3’.
II. Number of Rs. 20 notes that Dheeraj has is ‘9’.
III. Total value of Rs. 50 notes that Tushar has is Rs. 250.
Updated On: Aug 31, 2024
- Only II
- Only I
- Only I and III
- Only I and II
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The Correct Option is C
Solution and Explanation
Total amount with Dheeraj = Rs. 580
Total amount with Ritik = 580 – 350 = Rs. 230
Total amount with Prakash = 230 + 170 = Rs. 400
Total amount with Tushar = 1.125 × 400 = Rs. 450
Total amount with Sahil = 450 × (2/3) = Rs. 300
For Prakash:
Prakash has Rs. 400 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 400 – 100 = 300
So, the number of Rs. 50 denomination notes = \(\frac{300}{50}\)= 6
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 400 – 200 = 200
So, the number of Rs. 50 denomination notes = \(\frac{200}{50}\)= 4
But, the number of Rs. 50 notes with Prakash is more than the number of
Rs. 20 notes. So, case 2 is eliminated.
The number of notes of Rs. 20 and Rs. 50 denomination with Prakash is ‘5’ and ‘6’, respectively.
For Ritik:
Ritik has Rs. 230 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 1 × 50 = Rs. 50
Remaining amount = 230 – 50 = 180
So, the number of Rs. 20 denomination notes = 180/20 = 9
Case 2:
Let the number of Rs. 50 denomination notes = 2
So, the value of Rs. 50 denomination notes = 2 × 50 = Rs. 100
Remaining amount = 230 – 100 = 130
So, the number of Rs. 20 denomination notes = \(\frac{130}{2}\)= 6.5
This case is not possible.
Case 3:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 3 × 50 = Rs. 150
Remaining amount = 230 – 150 = 80
So, the number of Rs. 20 denomination notes = \(\frac{80}{20}\) = 4
Case 4:
Let the number of Rs. 50 denomination notes = 4
So, the value of Rs. 50 denomination notes = 4 × 50 = Rs. 200
Remaining amount = 230 – 200 = 30
So, the number of Rs. 20 denomination notes = \(\frac{30}{20}\) = 1.5
This case is not possible.
Case 5:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 5 × 50 = Rs. 250
This case is not possible.
For Sahil:
Sahil has Rs. 300 with him in the denominations of Rs. 20 and Rs. 100 only.
Since, amount corresponding to Rs. 100 notes will be in multiple of 100 only.
Therefore, number of notes of Rs. 20 should in multiple of 100 so that
total amount will also be in multiple on 100.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 300 – 100 = 200
So, the number of Rs. 100 denomination notes = \(\frac{200}{100}\) = 2
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 300 – 200 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
For Tushar:
Tushar has Rs. 450 with him in the denominations of Rs. 50 and Rs. 100 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 50 × 1 = Rs. 50
Remaining amount = 450 – 50 = 400
So, the number of Rs. 100 denomination notes = \(\frac{400}{100}\)= 4
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 2:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 50 × 3 = Rs. 150
Remaining amount = 450 – 150 = 300
So, the number of Rs. 100 denomination notes =\(\frac{300}{100}\)= 3
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 3:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 50 × 5 = Rs. 250
Remaining amount = 450 – 250 = 200
So, the number of Rs. 100 denomination notes =\(\frac{200}{100}\)= 2
This case is possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 4:
Let the number of Rs. 50 denomination notes = 7
So, the value of Rs. 50 denomination notes = 50 × 7 = Rs. 350
Remaining amount = 450 – 350 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Only possible case for Tushar:
The number of Rs. 50 denomination notes = 5
The number of Rs. 100 denomination notes = 2
Only possible case for Sahil:
The number of Rs. 20 denomination notes = 5
The number of Rs. 100 denomination notes = 2
For Dheeraj:
Dheeraj has Rs. 580 with him in the denominations of Rs. 20, Rs. 50 and Rs. 100 only.
The number of Rs. 20 denomination notes = 4 or 9
The total number of notes that Dheeraj has = 11
Case 1:
The number of Rs. 20 denomination notes = 4
So, the value of Rs. 20 denomination notes = 20 × 4 = Rs. 80
Remaining amount = 580 – 80 = 500
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 4 = 7
If the number of notes of Rs. 50 denomination will be 2 then the number of notes of Rs. 100 denomination will be 5. But this is not possible,
because then the total value of Rs. 50 and Rs. 100 notes together will be
Rs. 600.
If the number of notes of Rs. 50 denomination is 4, then the number of
notes of Rs. 100 denomination will be 3. And this is possible, because, the total value of Rs. 50 and Rs. 100 notes together will be Rs. 500.
If the number of notes of Rs. 50 denomination is 6, then the number of
notes of Rs. 100 denomination will be 1. And this is not possible, because,
the total value of Rs. 50 and Rs. 100 notes together will be Rs. 400.
Case 2:
The number of Rs. 20 denomination notes = 9
So, the value of Rs. 20 denomination notes = 20 × 9 = Rs. 180
Remaining amount = 580 – 180 = 400
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 9 = 2
The number of notes of Rs. 50 and Rs. 100 denomination is 1 each.
But this is not possible, because the total value of Rs. 50 and Rs. 100 notes together l be Rs. 150.
So, the number of Rs. 20 and Rs. 50 denomination notes with Ritik is 4 and 3, respectively.
And, the number of Rs. 20, Rs. 50 and Rs. 100 denomination notes of
Dheeraj is 4, 4 and 3, respectively.
Since, Ritik has ‘3’ Rs. 50 notes.
So, ‘I’ is true.
For ‘II’:
Since, Dheeraj has ‘4’ Rs. 20 notes.
So, ‘II’ is not true.
For ‘III’:
Since, total value of Rs. 50 notes that Tushar has is Rs. 250
So, ‘III’ is true.
So, the correct option is (C): Only I and III.
Total amount with Ritik = 580 – 350 = Rs. 230
Total amount with Prakash = 230 + 170 = Rs. 400
Total amount with Tushar = 1.125 × 400 = Rs. 450
Total amount with Sahil = 450 × (2/3) = Rs. 300
For Prakash:
Prakash has Rs. 400 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 400 – 100 = 300
So, the number of Rs. 50 denomination notes = \(\frac{300}{50}\)= 6
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 400 – 200 = 200
So, the number of Rs. 50 denomination notes = \(\frac{200}{50}\)= 4
But, the number of Rs. 50 notes with Prakash is more than the number of
Rs. 20 notes. So, case 2 is eliminated.
The number of notes of Rs. 20 and Rs. 50 denomination with Prakash is ‘5’ and ‘6’, respectively.
For Ritik:
Ritik has Rs. 230 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 1 × 50 = Rs. 50
Remaining amount = 230 – 50 = 180
So, the number of Rs. 20 denomination notes = 180/20 = 9
Case 2:
Let the number of Rs. 50 denomination notes = 2
So, the value of Rs. 50 denomination notes = 2 × 50 = Rs. 100
Remaining amount = 230 – 100 = 130
So, the number of Rs. 20 denomination notes = \(\frac{130}{2}\)= 6.5
This case is not possible.
Case 3:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 3 × 50 = Rs. 150
Remaining amount = 230 – 150 = 80
So, the number of Rs. 20 denomination notes = \(\frac{80}{20}\) = 4
Case 4:
Let the number of Rs. 50 denomination notes = 4
So, the value of Rs. 50 denomination notes = 4 × 50 = Rs. 200
Remaining amount = 230 – 200 = 30
So, the number of Rs. 20 denomination notes = \(\frac{30}{20}\) = 1.5
This case is not possible.
Case 5:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 5 × 50 = Rs. 250
This case is not possible.
For Sahil:
Sahil has Rs. 300 with him in the denominations of Rs. 20 and Rs. 100 only.
Since, amount corresponding to Rs. 100 notes will be in multiple of 100 only.
Therefore, number of notes of Rs. 20 should in multiple of 100 so that
total amount will also be in multiple on 100.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 300 – 100 = 200
So, the number of Rs. 100 denomination notes = \(\frac{200}{100}\) = 2
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 300 – 200 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
For Tushar:
Tushar has Rs. 450 with him in the denominations of Rs. 50 and Rs. 100 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 50 × 1 = Rs. 50
Remaining amount = 450 – 50 = 400
So, the number of Rs. 100 denomination notes = \(\frac{400}{100}\)= 4
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 2:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 50 × 3 = Rs. 150
Remaining amount = 450 – 150 = 300
So, the number of Rs. 100 denomination notes =\(\frac{300}{100}\)= 3
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 3:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 50 × 5 = Rs. 250
Remaining amount = 450 – 250 = 200
So, the number of Rs. 100 denomination notes =\(\frac{200}{100}\)= 2
This case is possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 4:
Let the number of Rs. 50 denomination notes = 7
So, the value of Rs. 50 denomination notes = 50 × 7 = Rs. 350
Remaining amount = 450 – 350 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Only possible case for Tushar:
The number of Rs. 50 denomination notes = 5
The number of Rs. 100 denomination notes = 2
Only possible case for Sahil:
The number of Rs. 20 denomination notes = 5
The number of Rs. 100 denomination notes = 2
For Dheeraj:
Dheeraj has Rs. 580 with him in the denominations of Rs. 20, Rs. 50 and Rs. 100 only.
The number of Rs. 20 denomination notes = 4 or 9
The total number of notes that Dheeraj has = 11
Case 1:
The number of Rs. 20 denomination notes = 4
So, the value of Rs. 20 denomination notes = 20 × 4 = Rs. 80
Remaining amount = 580 – 80 = 500
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 4 = 7
If the number of notes of Rs. 50 denomination will be 2 then the number of notes of Rs. 100 denomination will be 5. But this is not possible,
because then the total value of Rs. 50 and Rs. 100 notes together will be
Rs. 600.
If the number of notes of Rs. 50 denomination is 4, then the number of
notes of Rs. 100 denomination will be 3. And this is possible, because, the total value of Rs. 50 and Rs. 100 notes together will be Rs. 500.
If the number of notes of Rs. 50 denomination is 6, then the number of
notes of Rs. 100 denomination will be 1. And this is not possible, because,
the total value of Rs. 50 and Rs. 100 notes together will be Rs. 400.
Case 2:
The number of Rs. 20 denomination notes = 9
So, the value of Rs. 20 denomination notes = 20 × 9 = Rs. 180
Remaining amount = 580 – 180 = 400
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 9 = 2
The number of notes of Rs. 50 and Rs. 100 denomination is 1 each.
But this is not possible, because the total value of Rs. 50 and Rs. 100 notes together l be Rs. 150.
So, the number of Rs. 20 and Rs. 50 denomination notes with Ritik is 4 and 3, respectively.
And, the number of Rs. 20, Rs. 50 and Rs. 100 denomination notes of
Dheeraj is 4, 4 and 3, respectively.
| Persons | Number of notes of | ||
| Rs. 20 | Rs. 50 | Rs. 100 | |
| Prakash | 5 | 6 | - |
| Ritik | 4 | 3 | - |
| Sahil | 5 | - | 2 |
| Tushar | - | 5 | 2 |
| Dheeraj | 4 | 4 | 3 |
So, ‘I’ is true.
For ‘II’:
Since, Dheeraj has ‘4’ Rs. 20 notes.
So, ‘II’ is not true.
For ‘III’:
Since, total value of Rs. 50 notes that Tushar has is Rs. 250
So, ‘III’ is true.
So, the correct option is (C): Only I and III.
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Question: 4
Find the ratio of the total value of Rs. 50 notes that Prakash has to the total value of Rs. 100 notes that Dheeraj has.
Find the ratio of the total value of Rs. 50 notes that Prakash has to the total value of Rs. 100 notes that Dheeraj has.
Updated On: Aug 31, 2024
- 3:2
- 1:1
- 4:5
- 2:1
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The Correct Option is B
Solution and Explanation
Total amount with Dheeraj = Rs. 580
Total amount with Ritik = 580 – 350 = Rs. 230
Total amount with Prakash = 230 + 170 = Rs. 400
Total amount with Tushar = 1.125 × 400 = Rs. 450
Total amount with Sahil = 450 × (2/3) = Rs. 300
For Prakash:
Prakash has Rs. 400 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 400 – 100 = 300
So, the number of Rs. 50 denomination notes = \(\frac{300}{50}\)= 6
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 400 – 200 = 200
So, the number of Rs. 50 denomination notes = \(\frac{200}{50}\)= 4
But, the number of Rs. 50 notes with Prakash is more than the number of
Rs. 20 notes. So, case 2 is eliminated.
The number of notes of Rs. 20 and Rs. 50 denomination with Prakash is ‘5’ and ‘6’, respectively.
For Ritik:
Ritik has Rs. 230 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 1 × 50 = Rs. 50
Remaining amount = 230 – 50 = 180
So, the number of Rs. 20 denomination notes = 180/20 = 9
Case 2:
Let the number of Rs. 50 denomination notes = 2
So, the value of Rs. 50 denomination notes = 2 × 50 = Rs. 100
Remaining amount = 230 – 100 = 130
So, the number of Rs. 20 denomination notes = \(\frac{130}{2}\)= 6.5
This case is not possible.
Case 3:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 3 × 50 = Rs. 150
Remaining amount = 230 – 150 = 80
So, the number of Rs. 20 denomination notes = \(\frac{80}{20}\) = 4
Case 4:
Let the number of Rs. 50 denomination notes = 4
So, the value of Rs. 50 denomination notes = 4 × 50 = Rs. 200
Remaining amount = 230 – 200 = 30
So, the number of Rs. 20 denomination notes = \(\frac{30}{20}\) = 1.5
This case is not possible.
Case 5:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 5 × 50 = Rs. 250
This case is not possible.
For Sahil:
Sahil has Rs. 300 with him in the denominations of Rs. 20 and Rs. 100 only.
Since, amount corresponding to Rs. 100 notes will be in multiple of 100 only.
Therefore, number of notes of Rs. 20 should in multiple of 100 so that
total amount will also be in multiple on 100.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 300 – 100 = 200
So, the number of Rs. 100 denomination notes = \(\frac{200}{100}\) = 2
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 300 – 200 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
For Tushar:
Tushar has Rs. 450 with him in the denominations of Rs. 50 and Rs. 100 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 50 × 1 = Rs. 50
Remaining amount = 450 – 50 = 400
So, the number of Rs. 100 denomination notes = \(\frac{400}{100}\)= 4
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 2:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 50 × 3 = Rs. 150
Remaining amount = 450 – 150 = 300
So, the number of Rs. 100 denomination notes =\(\frac{300}{100}\)= 3
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 3:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 50 × 5 = Rs. 250
Remaining amount = 450 – 250 = 200
So, the number of Rs. 100 denomination notes =\(\frac{200}{100}\)= 2
This case is possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 4:
Let the number of Rs. 50 denomination notes = 7
So, the value of Rs. 50 denomination notes = 50 × 7 = Rs. 350
Remaining amount = 450 – 350 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Only possible case for Tushar:
The number of Rs. 50 denomination notes = 5
The number of Rs. 100 denomination notes = 2
Only possible case for Sahil:
The number of Rs. 20 denomination notes = 5
The number of Rs. 100 denomination notes = 2
For Dheeraj:
Dheeraj has Rs. 580 with him in the denominations of Rs. 20, Rs. 50 and Rs. 100 only.
The number of Rs. 20 denomination notes = 4 or 9
The total number of notes that Dheeraj has = 11
Case 1:
The number of Rs. 20 denomination notes = 4
So, the value of Rs. 20 denomination notes = 20 × 4 = Rs. 80
Remaining amount = 580 – 80 = 500
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 4 = 7
If the number of notes of Rs. 50 denomination will be 2 then the number of notes of Rs. 100 denomination will be 5. But this is not possible,
because then the total value of Rs. 50 and Rs. 100 notes together will be
Rs. 600.
If the number of notes of Rs. 50 denomination is 4, then the number of
notes of Rs. 100 denomination will be 3. And this is possible, because, the total value of Rs. 50 and Rs. 100 notes together will be Rs. 500.
If the number of notes of Rs. 50 denomination is 6, then the number of
notes of Rs. 100 denomination will be 1. And this is not possible, because,
the total value of Rs. 50 and Rs. 100 notes together will be Rs. 400.
Case 2:
The number of Rs. 20 denomination notes = 9
So, the value of Rs. 20 denomination notes = 20 × 9 = Rs. 180
Remaining amount = 580 – 180 = 400
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 9 = 2
The number of notes of Rs. 50 and Rs. 100 denomination is 1 each.
But this is not possible, because the total value of Rs. 50 and Rs. 100 notes together l be Rs. 150.
So, the number of Rs. 20 and Rs. 50 denomination notes with Ritik is 4 and 3, respectively.
And, the number of Rs. 20, Rs. 50 and Rs. 100 denomination notes of
Dheeraj is 4, 4 and 3, respectively.
Total value of Rs. 50 notes that Prakash has = 50 × 6 = Rs. 300
Total value of Rs. 100 notes that Dheeraj has = 100 × 3 = Rs. 300
Required ratio = 1:1
So, the correct option is (B) : 1:1
Total amount with Ritik = 580 – 350 = Rs. 230
Total amount with Prakash = 230 + 170 = Rs. 400
Total amount with Tushar = 1.125 × 400 = Rs. 450
Total amount with Sahil = 450 × (2/3) = Rs. 300
For Prakash:
Prakash has Rs. 400 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 400 – 100 = 300
So, the number of Rs. 50 denomination notes = \(\frac{300}{50}\)= 6
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 400 – 200 = 200
So, the number of Rs. 50 denomination notes = \(\frac{200}{50}\)= 4
But, the number of Rs. 50 notes with Prakash is more than the number of
Rs. 20 notes. So, case 2 is eliminated.
The number of notes of Rs. 20 and Rs. 50 denomination with Prakash is ‘5’ and ‘6’, respectively.
For Ritik:
Ritik has Rs. 230 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 1 × 50 = Rs. 50
Remaining amount = 230 – 50 = 180
So, the number of Rs. 20 denomination notes = 180/20 = 9
Case 2:
Let the number of Rs. 50 denomination notes = 2
So, the value of Rs. 50 denomination notes = 2 × 50 = Rs. 100
Remaining amount = 230 – 100 = 130
So, the number of Rs. 20 denomination notes = \(\frac{130}{2}\)= 6.5
This case is not possible.
Case 3:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 3 × 50 = Rs. 150
Remaining amount = 230 – 150 = 80
So, the number of Rs. 20 denomination notes = \(\frac{80}{20}\) = 4
Case 4:
Let the number of Rs. 50 denomination notes = 4
So, the value of Rs. 50 denomination notes = 4 × 50 = Rs. 200
Remaining amount = 230 – 200 = 30
So, the number of Rs. 20 denomination notes = \(\frac{30}{20}\) = 1.5
This case is not possible.
Case 5:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 5 × 50 = Rs. 250
This case is not possible.
For Sahil:
Sahil has Rs. 300 with him in the denominations of Rs. 20 and Rs. 100 only.
Since, amount corresponding to Rs. 100 notes will be in multiple of 100 only.
Therefore, number of notes of Rs. 20 should in multiple of 100 so that
total amount will also be in multiple on 100.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 300 – 100 = 200
So, the number of Rs. 100 denomination notes = \(\frac{200}{100}\) = 2
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 300 – 200 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
For Tushar:
Tushar has Rs. 450 with him in the denominations of Rs. 50 and Rs. 100 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 50 × 1 = Rs. 50
Remaining amount = 450 – 50 = 400
So, the number of Rs. 100 denomination notes = \(\frac{400}{100}\)= 4
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 2:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 50 × 3 = Rs. 150
Remaining amount = 450 – 150 = 300
So, the number of Rs. 100 denomination notes =\(\frac{300}{100}\)= 3
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 3:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 50 × 5 = Rs. 250
Remaining amount = 450 – 250 = 200
So, the number of Rs. 100 denomination notes =\(\frac{200}{100}\)= 2
This case is possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 4:
Let the number of Rs. 50 denomination notes = 7
So, the value of Rs. 50 denomination notes = 50 × 7 = Rs. 350
Remaining amount = 450 – 350 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Only possible case for Tushar:
The number of Rs. 50 denomination notes = 5
The number of Rs. 100 denomination notes = 2
Only possible case for Sahil:
The number of Rs. 20 denomination notes = 5
The number of Rs. 100 denomination notes = 2
For Dheeraj:
Dheeraj has Rs. 580 with him in the denominations of Rs. 20, Rs. 50 and Rs. 100 only.
The number of Rs. 20 denomination notes = 4 or 9
The total number of notes that Dheeraj has = 11
Case 1:
The number of Rs. 20 denomination notes = 4
So, the value of Rs. 20 denomination notes = 20 × 4 = Rs. 80
Remaining amount = 580 – 80 = 500
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 4 = 7
If the number of notes of Rs. 50 denomination will be 2 then the number of notes of Rs. 100 denomination will be 5. But this is not possible,
because then the total value of Rs. 50 and Rs. 100 notes together will be
Rs. 600.
If the number of notes of Rs. 50 denomination is 4, then the number of
notes of Rs. 100 denomination will be 3. And this is possible, because, the total value of Rs. 50 and Rs. 100 notes together will be Rs. 500.
If the number of notes of Rs. 50 denomination is 6, then the number of
notes of Rs. 100 denomination will be 1. And this is not possible, because,
the total value of Rs. 50 and Rs. 100 notes together will be Rs. 400.
Case 2:
The number of Rs. 20 denomination notes = 9
So, the value of Rs. 20 denomination notes = 20 × 9 = Rs. 180
Remaining amount = 580 – 180 = 400
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 9 = 2
The number of notes of Rs. 50 and Rs. 100 denomination is 1 each.
But this is not possible, because the total value of Rs. 50 and Rs. 100 notes together l be Rs. 150.
So, the number of Rs. 20 and Rs. 50 denomination notes with Ritik is 4 and 3, respectively.
And, the number of Rs. 20, Rs. 50 and Rs. 100 denomination notes of
Dheeraj is 4, 4 and 3, respectively.
| Persons | Number of notes of | ||
| Rs. 20 | Rs. 50 | Rs. 100 | |
| Prakash | 5 | 6 | - |
| Ritik | 4 | 3 | - |
| Sahil | 5 | - | 2 |
| Tushar | - | 5 | 2 |
| Dheeraj | 4 | 4 | 3 |
Total value of Rs. 100 notes that Dheeraj has = 100 × 3 = Rs. 300
Required ratio = 1:1
So, the correct option is (B) : 1:1
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Question: 5
Who among the following has the maximum number of Rs. 50 notes denomination?
Who among the following has the maximum number of Rs. 50 notes denomination?
Updated On: Aug 31, 2024
- Ritik
- Prakash
- Tushar
- Dheeraj
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Total amount with Dheeraj = Rs. 580
Total amount with Ritik = 580 – 350 = Rs. 230
Total amount with Prakash = 230 + 170 = Rs. 400
Total amount with Tushar = 1.125 × 400 = Rs. 450
Total amount with Sahil = 450 × (2/3) = Rs. 300
For Prakash:
Prakash has Rs. 400 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 400 – 100 = 300
So, the number of Rs. 50 denomination notes = \(\frac{300}{50}\)= 6
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 400 – 200 = 200
So, the number of Rs. 50 denomination notes = \(\frac{200}{50}\)= 4
But, the number of Rs. 50 notes with Prakash is more than the number of
Rs. 20 notes. So, case 2 is eliminated.
The number of notes of Rs. 20 and Rs. 50 denomination with Prakash is ‘5’ and ‘6’, respectively.
For Ritik:
Ritik has Rs. 230 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 1 × 50 = Rs. 50
Remaining amount = 230 – 50 = 180
So, the number of Rs. 20 denomination notes = 180/20 = 9
Case 2:
Let the number of Rs. 50 denomination notes = 2
So, the value of Rs. 50 denomination notes = 2 × 50 = Rs. 100
Remaining amount = 230 – 100 = 130
So, the number of Rs. 20 denomination notes = \(\frac{130}{2}\)= 6.5
This case is not possible.
Case 3:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 3 × 50 = Rs. 150
Remaining amount = 230 – 150 = 80
So, the number of Rs. 20 denomination notes = \(\frac{80}{20}\) = 4
Case 4:
Let the number of Rs. 50 denomination notes = 4
So, the value of Rs. 50 denomination notes = 4 × 50 = Rs. 200
Remaining amount = 230 – 200 = 30
So, the number of Rs. 20 denomination notes = \(\frac{30}{20}\) = 1.5
This case is not possible.
Case 5:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 5 × 50 = Rs. 250
This case is not possible.
For Sahil:
Sahil has Rs. 300 with him in the denominations of Rs. 20 and Rs. 100 only.
Since, amount corresponding to Rs. 100 notes will be in multiple of 100 only.
Therefore, number of notes of Rs. 20 should in multiple of 100 so that
total amount will also be in multiple on 100.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 300 – 100 = 200
So, the number of Rs. 100 denomination notes = \(\frac{200}{100}\) = 2
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 300 – 200 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
For Tushar:
Tushar has Rs. 450 with him in the denominations of Rs. 50 and Rs. 100 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 50 × 1 = Rs. 50
Remaining amount = 450 – 50 = 400
So, the number of Rs. 100 denomination notes = \(\frac{400}{100}\)= 4
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 2:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 50 × 3 = Rs. 150
Remaining amount = 450 – 150 = 300
So, the number of Rs. 100 denomination notes =\(\frac{300}{100}\)= 3
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 3:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 50 × 5 = Rs. 250
Remaining amount = 450 – 250 = 200
So, the number of Rs. 100 denomination notes =\(\frac{200}{100}\)= 2
This case is possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 4:
Let the number of Rs. 50 denomination notes = 7
So, the value of Rs. 50 denomination notes = 50 × 7 = Rs. 350
Remaining amount = 450 – 350 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Only possible case for Tushar:
The number of Rs. 50 denomination notes = 5
The number of Rs. 100 denomination notes = 2
Only possible case for Sahil:
The number of Rs. 20 denomination notes = 5
The number of Rs. 100 denomination notes = 2
For Dheeraj:
Dheeraj has Rs. 580 with him in the denominations of Rs. 20, Rs. 50 and Rs. 100 only.
The number of Rs. 20 denomination notes = 4 or 9
The total number of notes that Dheeraj has = 11
Case 1:
The number of Rs. 20 denomination notes = 4
So, the value of Rs. 20 denomination notes = 20 × 4 = Rs. 80
Remaining amount = 580 – 80 = 500
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 4 = 7
If the number of notes of Rs. 50 denomination will be 2 then the number of notes of Rs. 100 denomination will be 5. But this is not possible,
because then the total value of Rs. 50 and Rs. 100 notes together will be
Rs. 600.
If the number of notes of Rs. 50 denomination is 4, then the number of
notes of Rs. 100 denomination will be 3. And this is possible, because, the total value of Rs. 50 and Rs. 100 notes together will be Rs. 500.
If the number of notes of Rs. 50 denomination is 6, then the number of
notes of Rs. 100 denomination will be 1. And this is not possible, because,
the total value of Rs. 50 and Rs. 100 notes together will be Rs. 400.
Case 2:
The number of Rs. 20 denomination notes = 9
So, the value of Rs. 20 denomination notes = 20 × 9 = Rs. 180
Remaining amount = 580 – 180 = 400
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 9 = 2
The number of notes of Rs. 50 and Rs. 100 denomination is 1 each.
But this is not possible, because the total value of Rs. 50 and Rs. 100 notes together l be Rs. 150.
So, the number of Rs. 20 and Rs. 50 denomination notes with Ritik is 4 and 3, respectively.
And, the number of Rs. 20, Rs. 50 and Rs. 100 denomination notes of
Dheeraj is 4, 4 and 3, respectively.
Prakash has the maximum number of notes of Rs. 50 denomination.
So, the correct option is (B) : Prakash.
Total amount with Ritik = 580 – 350 = Rs. 230
Total amount with Prakash = 230 + 170 = Rs. 400
Total amount with Tushar = 1.125 × 400 = Rs. 450
Total amount with Sahil = 450 × (2/3) = Rs. 300
For Prakash:
Prakash has Rs. 400 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 400 – 100 = 300
So, the number of Rs. 50 denomination notes = \(\frac{300}{50}\)= 6
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 400 – 200 = 200
So, the number of Rs. 50 denomination notes = \(\frac{200}{50}\)= 4
But, the number of Rs. 50 notes with Prakash is more than the number of
Rs. 20 notes. So, case 2 is eliminated.
The number of notes of Rs. 20 and Rs. 50 denomination with Prakash is ‘5’ and ‘6’, respectively.
For Ritik:
Ritik has Rs. 230 with him in the denominations of Rs. 20 and Rs. 50 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 1 × 50 = Rs. 50
Remaining amount = 230 – 50 = 180
So, the number of Rs. 20 denomination notes = 180/20 = 9
Case 2:
Let the number of Rs. 50 denomination notes = 2
So, the value of Rs. 50 denomination notes = 2 × 50 = Rs. 100
Remaining amount = 230 – 100 = 130
So, the number of Rs. 20 denomination notes = \(\frac{130}{2}\)= 6.5
This case is not possible.
Case 3:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 3 × 50 = Rs. 150
Remaining amount = 230 – 150 = 80
So, the number of Rs. 20 denomination notes = \(\frac{80}{20}\) = 4
Case 4:
Let the number of Rs. 50 denomination notes = 4
So, the value of Rs. 50 denomination notes = 4 × 50 = Rs. 200
Remaining amount = 230 – 200 = 30
So, the number of Rs. 20 denomination notes = \(\frac{30}{20}\) = 1.5
This case is not possible.
Case 5:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 5 × 50 = Rs. 250
This case is not possible.
For Sahil:
Sahil has Rs. 300 with him in the denominations of Rs. 20 and Rs. 100 only.
Since, amount corresponding to Rs. 100 notes will be in multiple of 100 only.
Therefore, number of notes of Rs. 20 should in multiple of 100 so that
total amount will also be in multiple on 100.
Case 1:
Let the number of Rs. 20 denomination notes = 5
So, the value of Rs. 20 denomination notes = 5 × 20 = Rs. 100
Remaining amount = 300 – 100 = 200
So, the number of Rs. 100 denomination notes = \(\frac{200}{100}\) = 2
Case 2:
Let the number of Rs. 20 denomination notes = 10
So, the value of Rs. 20 denomination notes = 10 × 20 = Rs. 200
Remaining amount = 300 – 200 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
For Tushar:
Tushar has Rs. 450 with him in the denominations of Rs. 50 and Rs. 100 only.
Case 1:
Let the number of Rs. 50 denomination notes = 1
So, the value of Rs. 50 denomination notes = 50 × 1 = Rs. 50
Remaining amount = 450 – 50 = 400
So, the number of Rs. 100 denomination notes = \(\frac{400}{100}\)= 4
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 2:
Let the number of Rs. 50 denomination notes = 3
So, the value of Rs. 50 denomination notes = 50 × 3 = Rs. 150
Remaining amount = 450 – 150 = 300
So, the number of Rs. 100 denomination notes =\(\frac{300}{100}\)= 3
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 3:
Let the number of Rs. 50 denomination notes = 5
So, the value of Rs. 50 denomination notes = 50 × 5 = Rs. 250
Remaining amount = 450 – 250 = 200
So, the number of Rs. 100 denomination notes =\(\frac{200}{100}\)= 2
This case is possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Case 4:
Let the number of Rs. 50 denomination notes = 7
So, the value of Rs. 50 denomination notes = 50 × 7 = Rs. 350
Remaining amount = 450 – 350 = 100
So, the number of Rs. 100 denomination notes = \(\frac{100}{100}\) = 1
This case is not possible. Because, the number of notes that Sahil have is
same as the number of notes that Tushar have.
Only possible case for Tushar:
The number of Rs. 50 denomination notes = 5
The number of Rs. 100 denomination notes = 2
Only possible case for Sahil:
The number of Rs. 20 denomination notes = 5
The number of Rs. 100 denomination notes = 2
For Dheeraj:
Dheeraj has Rs. 580 with him in the denominations of Rs. 20, Rs. 50 and Rs. 100 only.
The number of Rs. 20 denomination notes = 4 or 9
The total number of notes that Dheeraj has = 11
Case 1:
The number of Rs. 20 denomination notes = 4
So, the value of Rs. 20 denomination notes = 20 × 4 = Rs. 80
Remaining amount = 580 – 80 = 500
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 4 = 7
If the number of notes of Rs. 50 denomination will be 2 then the number of notes of Rs. 100 denomination will be 5. But this is not possible,
because then the total value of Rs. 50 and Rs. 100 notes together will be
Rs. 600.
If the number of notes of Rs. 50 denomination is 4, then the number of
notes of Rs. 100 denomination will be 3. And this is possible, because, the total value of Rs. 50 and Rs. 100 notes together will be Rs. 500.
If the number of notes of Rs. 50 denomination is 6, then the number of
notes of Rs. 100 denomination will be 1. And this is not possible, because,
the total value of Rs. 50 and Rs. 100 notes together will be Rs. 400.
Case 2:
The number of Rs. 20 denomination notes = 9
So, the value of Rs. 20 denomination notes = 20 × 9 = Rs. 180
Remaining amount = 580 – 180 = 400
The number of Rs. 50 and Rs. 100 denomination notes = 11 – 9 = 2
The number of notes of Rs. 50 and Rs. 100 denomination is 1 each.
But this is not possible, because the total value of Rs. 50 and Rs. 100 notes together l be Rs. 150.
So, the number of Rs. 20 and Rs. 50 denomination notes with Ritik is 4 and 3, respectively.
And, the number of Rs. 20, Rs. 50 and Rs. 100 denomination notes of
Dheeraj is 4, 4 and 3, respectively.
| Persons | Number of notes of | ||
| Rs. 20 | Rs. 50 | Rs. 100 | |
| Prakash | 5 | 6 | - |
| Ritik | 4 | 3 | - |
| Sahil | 5 | - | 2 |
| Tushar | - | 5 | 2 |
| Dheeraj | 4 | 4 | 3 |
So, the correct option is (B) : Prakash.
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