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 then he gains Rs.\ 13. The actual price of the book (in Rs.) is:

Answer 1

Correct Answer: 3

Concept: This is a
profit and loss problem using simultaneous equations.
Step 1: Assume cost prices.
Let cost price of pen = \(x\), book = \(y\)
Step 2: Form first equation.
\[ \text{Loss on pen} = 5% \Rightarrow -0.05x \] \[ \text{Gain on book} = 15% \Rightarrow +0.15y \] \[ -0.05x + 0.15y = 7 \quad \cdots (1) \]
Step 3: Form second equation.
\[ \text{Gain on pen} = 5% \Rightarrow +0.05x \] \[ \text{Gain on book} = 10% \Rightarrow +0.10y \] \[ 0.05x + 0.10y = 13 \quad \cdots (2) \]
Step 4: Simplify equations.
Multiply both equations by 100: \[ -5x + 15y = 700 \quad \cdots (1) \] \[ 5x + 10y = 1300 \quad \cdots (2) \]
Step 5: Add equations.
\[ (-5x + 15y) + (5x + 10y) = 700 + 1300 \] \[ 25y = 2000 \Rightarrow y = 80 \]
Step 6: Option analysis.

• (A) 100: Incorrect $\times$
• (B) 60: Incorrect $\times$
• (C) 80: Correct \checkmark
• (D) 75: Incorrect $\times$
• (E) 95: Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (C).