Profit and Loss – Profit rises from 20% to 25% after a 25% SP hike: A retailer increases his selling price by 25%, and as a result his profit percentage rises from 20% to 25%. By what percentage did his cost price increase?

Introduction / Context:
We compare two periods: before and after a selling price hike. The initial profit% (on old cost) and the new profit% (on new cost) tie the two situations. The link is that SP after the change equals 1.25 times the original SP, which itself was tied to the original cost.

Given Data / Assumptions:

• Initial profit = 20% ⇒ SP1 = 1.20 * C1
• SP raised by 25% ⇒ SP2 = 1.25 * SP1
• New profit = 25% ⇒ SP2 = 1.25 * C2

Concept / Approach:
Equate SP2 from both expressions and solve for C2 in terms of C1. The percentage increase in cost is (C2 − C1)/C1 * 100.

Step-by-Step Solution:
SP2 = 1.25 * SP1 = 1.25 * (1.20 * C1) = 1.50 * C1But SP2 = 1.25 * C2Hence 1.25 * C2 = 1.50 * C1 ⇒ C2 = 1.20 * C1Increase% in cost = (1.20 − 1) * 100 = 20%

Verification / Alternative check:
Pick C1 = 100 ⇒ SP1 = 120. Raise SP by 25% ⇒ SP2 = 150. If C2 = 120, profit% = (150 − 120)/120 * 100 = 25% as stated.

Why Other Options Are Wrong:
30%, 25%, and 50% misstate the derived relation; 15% is too low.

Common Pitfalls:
Assuming profit change alone drives the result; the key is equating SP2 from both viewpoints.

Final Answer:
20%