Profit and Loss – Profit percent at two selling prices: The percentage profit when an article is sold for Rs 78 is twice the percentage profit when it is sold for Rs 69. What is the cost price of the article?

Introduction / Context:
We are comparing two percentage profits relative to the same cost price. Because percentage profit equals (SP − CP) / CP * 100, equating the ratio of the two profits to 2:1 yields a simple linear equation in CP.

Given Data / Assumptions:

• Profit% at SP = 78 is twice profit% at SP = 69
• Let CP = x

Concept / Approach:
(78 − x)/x = 2 * (69 − x)/x ⇒ 78 − x = 2(69 − x). Solve for x to obtain the cost price.

Step-by-Step Solution:
78 − x = 138 − 2x−x + 2x = 138 − 78x = 60

Verification / Alternative check:
At CP 60: profit at 78 = 18 ⇒ 30%; profit at 69 = 9 ⇒ 15%; indeed 30% is twice 15%.

Why Other Options Are Wrong:
49, 51, 57, and 54 do not satisfy the twice-as-large percentage relation.

Common Pitfalls:
Comparing rupee profits instead of percentage profits; the condition is on percentages, not amounts.

Final Answer:
Rs 60