The profit after selling a pair of trousers for Rs 863 is the same as the loss…

Concept: When one selling price gives a profit and a different selling price on the same item gives a loss of the exact same amount, the cost price is the arithmetic mean (average) of the two selling prices. This follows because profit = SP₁ − CP and loss = CP − SP₂, and setting profit = loss gives CP = (SP₁ + SP₂) / 2.

1. Let the cost price be CP. Then profit = 863 − CP and loss = CP − 631.

2. Since profit = loss: 863 − CP = CP − 631.

3. Solving: 863 + 631 = 2CP ⇒ 1494 = 2CP ⇒ CP = 747.

Cross-check: Profit = 863 − 747 = 116 and Loss = 747 − 631 = 116, confirming they are equal, so CP = 747 is correct. Since Rs 747 does not match any of the numeric options (750, 800, 763), the correct answer is "None of these".