Question

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.

• A. Rs. 360
• B. Rs. 450
• C. Rs. 420
• D. Rs. 300
• A. Rs. 600
• B. Rs. 480
• C. Rs. 300
• D. Rs. 800
• A. Rs. 2140
• B. Rs. 4080
• C. Rs. 2320
• D. Rs. 2640
• A. 480
• B. 400
• C. 500
• D. 600
• A. 130
• B. 170
• C. 150
• D. 190

Answer 1

The Correct Option is B

The correct option is (B) : Rs. 450
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

According to the question,
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.

Answer 2

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.

Answer 3

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

Answer 4

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.

Answer 5

The correct option is (B) : 170.
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.