On Selling A Pen At 5% Loss And A Book At 15% Gain, Karim Gains Rs. 7 GMAT Problem Solving

Question: On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs. 7. If he sells the pen at 5% gain and the book at 10% gain, he gains Rs. 13. What is the cost price of the book in Rupees?

A)75
B)80
C)85
D)95
E)100

“On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs. 7”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”.

The candidates must learn the mathematical aptitudes in order to crack GMAT Problem Solving questions. GMAT quant evaluates the mathematical and analytical concepts of the candidates. The candidates have to master basic maths and use logic to solve the question. The candidate has to choose the correct option by resolving the question mathematically. The GMAT Quant topic in the problem-solving part includes highly calculative mathematical problems that need better qualitative skills to solve them.

Solution and Explanation:

Approach Solution 1:

The problem statement informs that
Given:

• Karim gains Rs. 7 on selling a pen at a 5% loss and a book at a 15% gain.
• He gains Rs. 13 if he sells the pen at a 5% gain and the book at a 10% gain.

Find Out:

• The cost price of the book

Assume the cost price of the pen is P and the cost price of the book is B.
By selling a pen at 5%loss and a book at a 15% gain. Kareem gets 7 rupees as profit.
Therefore, the equation will be:
-0.05P+0.15B=7 -----(i)
By selling a pen at a 5% gain and a book at a 10% gain. Kareem gains 13 rupees.
0.05P+0.10B=13 -----(ii)
By equating both the equation, we get
0.25B=20
Therefore, B=80
Thus the cost price of the book is 80.
Hence option B is the correct answer.

Correct Answer: B

Approach Solution 2:

The problem statement discloses that
Given:

• Karim gets Rs. 7 as profit on selling a pen at a 5% loss and a book at a 15% gain.
• If he sells the pen at a 5% gain and the book at a 10% gain, he gets Rs. 13 as a profit.

Find Out:

• The cost price of the book

Let the cost price of the pen be p and the cost price of the book be b.
According to the question, 0.15 b - 0.05 p = 7
Or, we can say, 15b – 5p = 700 …..(i)
Similarly, as per the question, we get, 10b + 5p = 1300 ….(ii)
By adding both equations we will get, 25b = 2000
Or we can say, b = 2000/25 = 80
Therefore, the cost price of the book is rupees 80.
Hence option B is the correct answer.

Correct Answer: B

Approach Solution 3:

The problem statement suggests that

• On selling a pen at a 5% loss and a book at a 15% gain, Karim gets Rs. 7 as profit.
• If Kareem sells the pen at a 5% gain and the book at a 10% gain, he gets Rs. 13 as a profit.

Asked: What is the cost price of the book?
Let's assume the cost price of a pen is 100p and the cost price of a book is 100b
Therefore, on selling the pen at a loss of 5% and a book at a profit of 15%, the net profit will be:
-5p + 15b = 7….(i)
Furthermore, if he sells the pe at a profit of 5% and the book at a profit of 10%, the net profit will be:
5p + 10b = 13 ….(ii)
By adding both equations (i) and (ii), we get,
25b = 20
Therefore, we can say, 100b = 20 * 4 = 80
Thus the cost price of the books is rupees 80.
Hence option B is the correct answer.

Correct Answer: B

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