On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs. 7. If he…
2025
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?
Answer: A. 80 — Concept: When two items are sold together under two different profit/loss scenarios, each scenario's total rupee gain gives one linear equation in the two…
- A.
80
- B.
85
- C.
100
- D.
95
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Correct answer: A
Concept: When two items are sold together under two different profit/loss scenarios, each scenario's total rupee gain gives one linear equation in the two unknown cost prices — a loss contributes a negative percentage-of-cost-price term and a gain a positive one. Two such equations in two unknowns can be solved by elimination: add or subtract them to cancel one variable and isolate the other.
Setting up the equations:
Let P = cost price of the pen and b = cost price of the book.
First sale: pen at 5% loss and book at 15% gain gives a total gain of Rs. 7, so −0.05P + 0.15b = 7 (Equation 1).
Second sale: pen at 5% gain and book at 10% gain gives a total gain of Rs. 13, so 0.05P + 0.10b = 13 (Equation 2).
Adding Equation 1 and Equation 2 cancels the pen's terms (−0.05P and +0.05P) exactly, leaving 0.25b = 20.
Solving, b = 20 ÷ 0.25 = Rs. 80.
Cross-check: substitute b = 80 into Equation 2: 0.05P + 0.10(80) = 13, so 0.05P = 5 and P = 100. Checking in Equation 1: −0.05(100) + 0.15(80) = −5 + 12 = 7, which matches. Both equations hold, confirming the book's cost price is Rs. 80 (and the pen's cost price is Rs. 100).