Anil purchases two books for Rs. 100. He sells the first book at a loss of 5%…

Concept

In a combined-transaction profit-and-loss problem, when a total cost is split between two parts sold at different loss and profit percentages, the unknown split is found by equating the sum of the two individual selling prices to the total selling price implied by the stated overall profit or loss percentage.

Application

Let the cost of the first book be x, so the cost of the second book is (100 − x).

1. Selling price of the first book at 5% loss = 0.95x

2. Selling price of the second book at 20% profit = 1.20 × (100 − x)

3. An overall profit of 5% on the combined cost of Rs. 100 means the total selling price must be Rs. 105

4. Equation: 0.95x + 1.20(100 − x) = 105

5. Expand: 0.95x + 120 − 1.20x = 105

6. Combine like terms: −0.25x = −15

7. Solve: x = 60

Cross-check

Cross-check with the alligation (weighted-average) rule: comparing the two percentages, −5% and 20%, against the overall 5%, the ratio of the first book's cost to the second book's cost is 15 : 10, that is 3 : 2, so the first book's cost is three-fifths of Rs. 100, which is Rs. 60 — confirming the algebraic result.

The cost price of the first book is Rs. 60.