Profit and Loss – Percentage gain equals cost price (in rupees): By selling an article for Rs 144, a man gains such that the numerical value of the percentage gain equals the cost price. What is the cost price of the article?

Introduction / Context:
The phrase “percentage gain equals the cost price” means the numerical value of gain% equals CP measured in rupees. This leads to a quadratic equation in CP.

Given Data / Assumptions:

• SP = Rs 144
• Let CP = x
• Gain% (numerical) = x

Concept / Approach:
Gain = SP - CP. Also, Gain% = (Gain / CP) * 100. Set Gain% = x and solve.

Step-by-Step Solution:
Gain = 144 - x(144 - x) / x * 100 = x14400 - 100x = x^2 ⇒ x^2 + 100x - 14400 = 0Discriminant = 10000 + 57600 = 67600 ⇒ sqrt = 260x = (-100 + 260) / 2 = 80 (reject negative root)

Verification / Alternative check:
CP = 80 ⇒ Gain = 64 ⇒ Gain% = 64 / 80 * 100 = 80, which equals CP numerically.

Why Other Options Are Wrong:
60, 64, 72, 96 do not satisfy the quadratic relation.

Common Pitfalls:
Interpreting “equals” as rupees-to-rupees rather than a numerical equality of percentage and CP value.

Final Answer:
Rs 80