If a discount of 10% is given on the marked price of a book, the publisher gains 20%. If the discount is increased to 15%, the ga…

Question

If a discount of 10% is given on the marked price of a book, the publisher gains 20%. If the discount is increased to 15%, the gain of the publisher is?

1. A. 12%
2. B. 13 1/3% (Correct answer)
3. C. 11 1/3%
4. D. 10%

Correct Answer

Option B — B

Detailed Solution & Explanation

The correct answer is Option B.

Key Points

• Let the marked price be 100.
• A 10% discount gives a selling price of 90, and this yields a 20% gain, so the cost price is:
• CP = 90 / 1.20 = 75.
• Now apply a 15% discount: new selling price = 85. The gain is:
• Gain = 85 − 75 = 10, on a cost of 75 → (10/75) × 100 = 40/3 = 13 1/3 %.

Exam Tip

• always find the cost price first from the given discount-and-gain, then recompute the gain at the new discount.
• CP is the anchor that does not change.

Additional Information

• Set the marked price at 100 and work through cost price: a 10% discount gives SP 90 at a 20% gain, so CP = 90/1.2 = 75.
• With a 20% discount, SP = 80, so the gain is (80 − 75)/75 = 6.67%.
• The general relation to remember: SP = MP × (1 − d) and SP = CP × (1 + p), so CP = MP(1 − d)/(1 + p).