Alternate buy and sell plan — linking two scenarios to recover CP An article is sold at a 10% loss. If instead it had been bought for 20% less and then sold for Rs 55 more than the original selling price, the profit would have been 40%. What is the original cost price?

Introduction / Context:Two linked scenarios are provided: (1) original sale at 10% loss; (2) hypothetical: buy cheaper (−20% on CP) and sell Rs 55 higher than the original SP, resulting in +40% profit. Setting up both expressions allows solving for the original CP.

Given Data / Assumptions:

• Let original CP = x.
• Original SP = 0.90x (10% loss).
• Alternate CP' = 0.80x; Alternate SP' = 0.90x + 55 with profit 40% on CP'.

Concept / Approach:Profit in the alternate plan: (SP' − CP')/CP' = 0.40. Substitute CP' and SP' in terms of x and solve for x.

Step-by-Step Solution:(0.90x + 55 − 0.80x) / (0.80x) = 0.40.(0.10x + 55) / 0.80x = 0.40 ⇒ 0.10x + 55 = 0.32x.55 = 0.22x ⇒ x = 55 / 0.22 = 250.

Verification / Alternative check:Original SP = 225 (loss 10% on 250). Alternate CP' = 200; Alternate SP' = 225 + 55 = 280; Profit on 200 = 80 = 40% (checks out).

Why Other Options Are Wrong:200 or 225 do not satisfy both scenarios simultaneously; 'None of these' is false because 250 works; 275 is inconsistent.

Common Pitfalls:Adding/subtracting percentage points on prices rather than forming equations on CP and SP for each scenario.

Final Answer:Rs 250