Selling the same article at Rs 900 yields a profit equal to twice the loss incurred when selling it at Rs 490. At what price should it be sold to earn a 25% profit?

Introduction / Context:
A linear relation links profit at one selling price to loss at another when the cost price (CP) is fixed. Once CP is found, any target-gain selling price is straightforward.

Given Data / Assumptions:

• Selling price (SP₁) = Rs 900 with profit P.
• Selling price (SP₂) = Rs 490 with loss L.
• P = 2L (profit is double the loss).
• We want SP for 25% profit.

Concept / Approach:
Let CP = x. Then P = 900 − x and L = x − 490. Given P = 2L, solve for x. Then required price for 25% profit is 1.25x.

Step-by-Step Solution:

Verification / Alternative check:
Check P at Rs 900 is ≈ 273.33; L at Rs 490 is ≈ 136.67; indeed P ≈ 2L.

Why Other Options Are Wrong:
Rs 750, 775, 800, 825 do not equal 2350/3 and would not give exactly 25% on the computed CP.

Common Pitfalls:
Setting P = L instead of P = 2L or computing 25% profit on the selling price instead of CP.

Final Answer:
Rs 783.33