There are four sellers namely Ram, Mohan, Lakhan and Raghav. Each of them has three types of articles (pen, pencil and erasers). The given table shows the sum of the cost prices (in Rs.) of each pen and pencil, difference between total cost prices (in Rs.) of all the pencils and erasers and sum of cost prices (in Rs.) of all the pens and erasers, with the respective sellers.
| Sellers | Sum of the cost price (in Rs.) of each pen and pencil | Cost price (in Rs.) of all pencils - Cost price (in Rs.) of all erasers | Sum of cost price (in Rs.) of all pens and erasers |
| Ram | 15 | 100 | 2100 |
| Mohan | 13 | 480 | 2050 |
| Lakhan | 27 | 600 | 3000 |
| Raghav | 19 | 300 | 3300 |
Note : Number of pens/pencils/erasers sold by each of the given sellers is an integer.
Out of total number of erasers with Ram, 180 remained unsold while he sold rest of the erasers at a profit of 25% each. If cost price of each eraser for Ram is Rs. 7 less than cost price of each pen for him, then find the selling price of all the erasers sold by him.
- Rs. 360
- Rs. 450
- Rs. 420
- Rs. 300
The Correct Option is B
Solution and Explanation
For Ram:
Let the number of pencils with him be ‘x’ and cost price of each pencil be Rs. ‘a’
Therefore, total cost price of all the pencils = Rs. ax
Total cost price of all the erasers = Rs. (ax – 100)
Total cost price of all the pens = 2100 – (ax – 100) = Rs. (2200 – ax)
Therefore, sum of cost price of all the pen and pencils = 2200 – ax + ax = Rs. 2200
Also, cost price of each pen = Rs. (15 – a)
Case 1: Let the number of pen be more than that of pencils
Therefore, number of pens = Rs. (x + 80)
According to the question,
(15 – a) × (x + 80) + ax = 2200
Or, 15x – 80a = 1000...... (1)
Or, x + a = 205...... (2)
On solving equation (1) and (2), we get
Cost price of each pencil = Rs. 2075/65 (not possible)
Case 2: Let the number of pen sold be less than number of pencils
Therefore, number of pens = (x – 80)
According to the question,
(x – 80) × (15 – a) + ax = 2200
Or, 15x + 80a = 3400.......... (3)
Also, x + a = 205...... (4)
On solving equation (3) and (4), we get
Cost price of each pencil = Rs. 5
Number of pencils = 200
Total cost price of all the pencils = 200 × 5 = Rs. 1000
Cost price of each pen = Rs. 10
Number pens = 120
Total cost price of all the pen = 120 × 10 = Rs. 1200
Total cost price of all the erasers = 1000 – 100 = Rs. 900
| Number of pens | Cost price (in Rs.) of each pen | Number of pencils | Cost price (in Rs.) of each pencil | Total cost price (in Rs.) of all erasers | |
| Ram | 120 | 10 | 200 | 5 | 900 |
| Mohan | 250 | 5 | 160 | 8 | 800 |
| Lakhan | 150 | 12 | 120 | 15 | 1200 |
| Raghav | 200 | 15 | 150 | 4 | 300 |
Cost price of each eraser = 10 – 7 = Rs. 3
Therefore, number of erasers with Ram = \(\frac{900}{3} \)= 300
Number of erasers sold = 300 – 180 = 120
Required selling price = 1.25 × 120 × 3 = Rs. 450.
If Mohan sold certain number of pencils which is equal to the difference between number of pencils with him and Ram, at 50% profit after giving a discount of 20%, then find the marked price of all the pencils sold by him.
- Rs. 600
- Rs. 480
- Rs. 300
- Rs. 800
The Correct Option is A
Solution and Explanation
The correct option is (A) : Rs. 600.
For Ram:
Let the number of pencils with him be ‘x’ and cost price of each pencil be Rs. ‘a’
Therefore, total cost price of all the pencils = Rs. ax
Total cost price of all the erasers = Rs. (ax – 100)
Total cost price of all the pens = 2100 – (ax – 100) = Rs. (2200 – ax)
Therefore, sum of cost price of all the pen and pencils = 2200 – ax + ax = Rs. 2200
Also, cost price of each pen = Rs. (15 – a)
Case 1: Let the number of pen be more than that of pencils
Therefore, number of pens = Rs. (x + 80)
According to the question,
(15 – a) × (x + 80) + ax = 2200
Or, 15x – 80a = 1000...... (1)
Or, x + a = 205...... (2)
On solving equation (1) and (2), we get
Cost price of each pencil = Rs. \(\frac{2075}{65}\) (not possible)
Case 2: Let the number of pen sold be less than number of pencils
Therefore, number of pens = (x – 80)
According to the question,
(x – 80) × (15 – a) + ax = 2200
Or, 15x + 80a = 3400.......... (3)
Also, x + a = 205...... (4)
On solving equation (3) and (4), we get
Cost price of each pencil = Rs. 5
Number of pencils = 200
Total cost price of all the pencils = 200 × 5 = Rs. 1000
Cost price of each pen = Rs. 10
Number pens = 120
Total cost price of all the pen = 120 × 10 = Rs. 1200
Total cost price of all the erasers = 1000 – 100 = Rs. 900
| Number of pens | Cost price (in Rs.) of each pen | Number of pencils | Cost price (in Rs.) of each pencil | Total cost price (in Rs.) of all erasers | |
| Ram | 120 | 10 | 200 | 5 | 900 |
| Mohan | 250 | 5 | 160 | 8 | 800 |
| Lakhan | 150 | 12 | 120 | 15 | 1200 |
| Raghav | 200 | 15 | 150 | 4 | 300 |
Number of pencils sold by Mohan = 200 – 160 = 40
Selling price of 40 pencils = 1.5 × 8 × 40 = Rs. 480
Marked price of 40 pencils =\(\frac{480}{0.8}\)= Rs. 600.
If the cost price of each pen for Lakhan had been Rs. 2 less, then the cost price of each eraser with him would have been 85% less than that of each pen with him. Find the sum of selling price of all the pencils and 120 erasers with Lakhan such that he sold each pencil at 20% profit and each eraser at profit of Rs. 2.5.
- Rs. 2140
- Rs. 4080
- Rs. 2320
- Rs. 2640
The Correct Option is D
Solution and Explanation
The correct option is (D) : Rs. 2640.
For Ram:
Let the number of pencils with him be ‘x’ and cost price of each pencil be Rs. ‘a’
Therefore, total cost price of all the pencils = Rs. ax
Total cost price of all the erasers = Rs. (ax – 100)
Total cost price of all the pens = 2100 – (ax – 100) = Rs. (2200 – ax)
Therefore, sum of cost price of all the pen and pencils = 2200 – ax + ax = Rs. 2200
Also, cost price of each pen = Rs. (15 – a)
Case 1: Let the number of pen be more than that of pencils
Therefore, number of pens = Rs. (x + 80)
According to the question,
(15 – a) × (x + 80) + ax = 2200
Or, 15x – 80a = 1000...... (1)
Or, x + a = 205...... (2)
On solving equation (1) and (2), we get
Cost price of each pencil = Rs. \(\frac{2075}{65}\) (not possible)
Case 2: Let the number of pen sold be less than number of pencils
Therefore, number of pens = (x – 80)
According to the question,
(x – 80) × (15 – a) + ax = 2200
Or, 15x + 80a = 3400.......... (3)
Also, x + a = 205...... (4)
On solving equation (3) and (4), we get
Cost price of each pencil = Rs. 5
Number of pencils = 200
Total cost price of all the pencils = 200 × 5 = Rs. 1000
Cost price of each pen = Rs. 10
Number pens = 120
Total cost price of all the pen = 120 × 10 = Rs. 1200
Total cost price of all the erasers = 1000 – 100 = Rs. 900
| Number of pens | Cost price (in Rs.) of each pen | Number of pencils | Cost price (in Rs.) of each pencil | Total cost price (in Rs.) of all erasers | |
| Ram | 120 | 10 | 200 | 5 | 900 |
| Mohan | 250 | 5 | 160 | 8 | 800 |
| Lakhan | 150 | 12 | 120 | 15 | 1200 |
| Raghav | 200 | 15 | 150 | 4 | 300 |
According to the question,
Cost price of each eraser with Lakhan = 0.85 × (12 – 2) = Rs. 1.5
Required sum = 1.2 × 15 ×120 + (1.5 + 2.5) × 120 = 2160 + 480 = Rs. 2640
Find the average number of erasers with Ram, Mohan and Lakhan such that cost price of each eraser with Ram is Rs. 3 which is Re. 1 more than cost price of each eraser with Mohan and twice the cost price of each eraser with Lakhan.
- 480
- 400
- 500
- 600
The Correct Option is C
Solution and Explanation
The correct option is (C) : 500
For Ram:
Let the number of pencils with him be ‘x’ and cost price of each pencil be Rs. ‘a’
Therefore, total cost price of all the pencils = Rs. ax
Total cost price of all the erasers = Rs. (ax – 100)
Total cost price of all the pens = 2100 – (ax – 100) = Rs. (2200 – ax)
Therefore, sum of cost price of all the pen and pencils = 2200 – ax + ax = Rs. 2200
Also, cost price of each pen = Rs. (15 – a)
Case 1: Let the number of pen be more than that of pencils
Therefore, number of pens = Rs. (x + 80)
According to the question,
(15 – a) × (x + 80) + ax = 2200
Or, 15x – 80a = 1000...... (1)
Or, x + a = 205...... (2)
On solving equation (1) and (2), we get
Cost price of each pencil = Rs. \(\frac{2075}{65}\) (not possible)
Case 2: Let the number of pen sold be less than number of pencils
Therefore, number of pens = (x – 80)
According to the question,
(x – 80) × (15 – a) + ax = 2200
Or, 15x + 80a = 3400.......... (3)
Also, x + a = 205...... (4)
On solving equation (3) and (4), we get
Cost price of each pencil = Rs. 5
Number of pencils = 200
Total cost price of all the pencils = 200 × 5 = Rs. 1000
Cost price of each pen = Rs. 10
Number pens = 120
Total cost price of all the pen = 120 × 10 = Rs. 1200
Total cost price of all the erasers = 1000 – 100 = Rs. 900
| Number of pens | Cost price (in Rs.) of each pen | Number of pencils | Cost price (in Rs.) of each pencil | Total cost price (in Rs.) of all erasers | |
| Ram | 120 | 10 | 200 | 5 | 900 |
| Mohan | 250 | 5 | 160 | 8 | 800 |
| Lakhan | 150 | 12 | 120 | 15 | 1200 |
| Raghav | 200 | 15 | 150 | 4 | 300 |
According to the question,
Number of erasers with Ram = \(\frac{900}{3}\)= 300
Number of erasers with Mohan = {\(\frac{800}{(3 – 1)}\)} = 400
Number of erasers with Lakhan = {\(\frac{(1200 × 2)}{3}\)} = 800
Required average = {\(\frac{(300 + 400 + 800)}{3}\)} = 500.
Find the average number of pencils with Ram, Mohan ad Raghav together.
- 130
- 170
- 150
- 190
The Correct Option is B
Solution and Explanation
For Ram:
Let the number of pencils with him be ‘x’ and cost price of each pencil be Rs. ‘a’
Therefore, total cost price of all the pencils = Rs. ax
Total cost price of all the erasers = Rs. (ax – 100)
Total cost price of all the pens = 2100 – (ax – 100) = Rs. (2200 – ax)
Therefore, sum of cost price of all the pen and pencils = 2200 – ax + ax = Rs. 2200
Also, cost price of each pen = Rs. (15 – a)
Case 1: Let the number of pen be more than that of pencils
Therefore, number of pens = Rs. (x + 80)
According to the question,
(15 – a) × (x + 80) + ax = 2200
Or, 15x – 80a = 1000...... (1)
Or, x + a = 205...... (2)
On solving equation (1) and (2), we get
Cost price of each pencil = Rs. \(\frac{2075}{65}\) (not possible)
Case 2: Let the number of pen sold be less than number of pencils
Therefore, number of pens = (x – 80)
According to the question,
(x – 80) × (15 – a) + ax = 2200
Or, 15x + 80a = 3400.......... (3)
Also, x + a = 205...... (4)
On solving equation (3) and (4), we get
Cost price of each pencil = Rs. 5
Number of pencils = 200
Total cost price of all the pencils = 200 × 5 = Rs. 1000
Cost price of each pen = Rs. 10
Number pens = 120
Total cost price of all the pen = 120 × 10 = Rs. 1200
Total cost price of all the erasers = 1000 – 100 = Rs. 900
| Number of pens | Cost price (in Rs.) of each pen | Number of pencils | Cost price (in Rs.) of each pencil | Total cost price (in Rs.) of all erasers | |
| Ram | 120 | 10 | 200 | 5 | 900 |
| Mohan | 250 | 5 | 160 | 8 | 800 |
| Lakhan | 150 | 12 | 120 | 15 | 1200 |
| Raghav | 200 | 15 | 150 | 4 | 300 |
Desired average = \(\frac{(200 + 160 + 150)}{3}\) = 170.
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