An article was sold for ₹322, yielding a gain equal to one-sixth of the outlay (cost). Find the cost price of the article.

Introduction / Context:“Gain equal to 1/6 of outlay” means the profit is 1/6 of cost price (CP). Therefore, selling price (SP) equals CP plus CP/6 = (7/6)CP. We invert this to find CP from the given SP.

Given Data / Assumptions:

• SP = ₹322.
• SP = (7/6) * CP.

Concept / Approach:Rearrange CP = SP * (6/7). This is a simple proportional relation.

Step-by-Step Solution:CP = 322 * (6/7) = 1932 / 7 = ₹276

Verification / Alternative check:Check: Profit = 322 − 276 = ₹46, which is 1/6 of 276 (since 276/6 = 46). Correct.

Why Other Options Are Wrong:₹300/₹376/₹175 do not satisfy SP = (7/6)CP with SP = ₹322.

Common Pitfalls:Using 1/6 of SP instead of CP; mishandling the fraction inversion when solving for CP.

Final Answer:₹ 276