A man purchased a watch for Rs 400 and sold it at a gain of 20% of the selling…

Concept: When a profit (gain) is stated as a percentage of the Selling Price (SP) rather than the Cost Price (CP), the relation becomes SP = CP + (gain% of SP), which rearranges to SP × (1 − gain%) = CP, i.e. SP = CP ÷ (1 − gain%). This differs from the more common case where the gain% is calculated on CP (SP = CP × (1 + gain%)).

Application:

1. Cost Price (CP) = Rs 400, and the gain equals 20% of the Selling Price (SP).

2. Set up the relation: SP = CP + 20% of SP, i.e. SP = 400 + 0.20 × SP.

3. Collect SP terms on one side: SP − 0.20 × SP = 400, i.e. 0.80 × SP = 400.

4. Solve for SP: SP = 400 ÷ 0.80 = 500.

Cross-check: Gain = SP − CP = 500 − 400 = 100. Is 100 equal to 20% of the selling price? 20% of 500 = 100 — yes, it matches, confirming the value is consistent with the stated condition.

So the selling price of the watch is Rs 500.