Profit and Loss – Markup with a small cash discount: A tradesman marks goods 30% above cost price. If he allows a discount of 6 1/4% on the marked price, what is his gain percentage?

Introduction / Context:
A marked-up price reduced by a small discount still yields a profit if the net multiplier relative to cost exceeds 1. We convert both the markup and the discount to multiplicative factors to find the exact net gain.

Given Data / Assumptions:

• Markup = 30% ⇒ MP = 1.30 * CP
• Discount = 6 1/4% = 6.25% ⇒ SP = 0.9375 * MP

Concept / Approach:
SP/CP = 1.30 * 0.9375 = 1.21875. Gain% = (1.21875 − 1) * 100 = 21.875%, which is 21 7/8% as a mixed fraction.

Step-by-Step Solution:
SP = 1.30 * 0.9375 * CP = 1.21875 * CPGain% = 0.21875 * 100 = 21.875% = 21 7/8%

Verification / Alternative check:
Let CP = ₹ 100; then MP = ₹ 130; after discount, SP = ₹ 121.875; gain = ₹ 21.875 ⇒ 21.875%.

Why Other Options Are Wrong:
23 3/4% and 22% are close but incorrect; 20% and 25% do not match the product factor.

Common Pitfalls:
Subtracting 6.25 from 30 to get 23.75% without accounting for the discount being applied to MP, not CP.

Final Answer:
21 7/8%