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. 80
• B. 85
• C. 95
• D. 100

Answer 1

The Correct Option is A

Let the cost price of a pen be \( x \) and that of a book be \( y \). 

The first condition is: \[ 0.95x + 1.15y = x + y + 7 \tag{1} \]

The second condition is: \[ 1.05x + 1.10y = x + y + 13 \tag{2} \]

Rearranging Equation (1): \[ 0.95x + 1.15y - x - y = 7 \\ -0.05x + 0.15y = 7 \tag{3} \]

Rearranging Equation (2): \[ 1.05x + 1.10y - x - y = 13 \\ 0.05x + 0.10y = 13 \tag{4} \]

Now add equations (3) and (4): \[ (-0.05x + 0.15y) + (0.05x + 0.10y) = 7 + 13 \\ 0.25y = 20 \Rightarrow y = 80 \]

Answer:

The cost price of the book is ₹80.