A book seller gives discount successively at the rate 25% and 16% on a book.…

CONCEPT: When two discounts are applied successively (one after the other), the final price is not the marked price reduced by the simple sum of the two percentages. Each discount acts on the price left after the previous discount, so the overall retained fraction of the marked price is the PRODUCT of the two individual retained fractions: retained fraction = (1 − first discount/100) × (1 − second discount/100).

Applying this to the question:

1. Let the actual (marked) price of the book be P.

2. After the first successive discount of 25%, the retained price is P × (1 − 25/100) = 0.75P.

3. The second successive discount of 16% is applied to this already-reduced price (not to the original price P): 0.75P × (1 − 16/100) = 0.75P × 0.84 = 0.63P.

4. This final amount equals the selling price stated in the question: 0.63P = Rs. 63.

5. Solving for P: P = 63 ÷ 0.63 = Rs. 100.

CROSS-CHECK: Apply the two discounts forward on Rs. 100 to confirm. A 25% discount on Rs. 100 leaves Rs. 75. A further 16% discount on Rs. 75 removes Rs. 12, leaving Rs. 63 — which matches the selling price given in the question, confirming the result.

So the actual (marked) price of the book is Rs. 100.