An article when sold at a gain of 5% yields Rs. 20 more than when sold at a…

When the same article is sold once at a gain of g% and once at a loss of l% on the same cost price, the difference between the two selling prices always equals (g + l)% of the cost price. This follows directly from Selling Price = Cost Price × (1 ± percentage/100).

1. Let the cost price of the article be Rs. x.

2. Selling price at a 5% gain = x + 5% of x = 1.05x.

3. Selling price at a 5% loss = x − 5% of x = 0.95x.

4. Difference between the two selling prices = 1.05x − 0.95x = 0.10x.

5. This difference is given as Rs. 20, so 0.10x = 20, which gives x = 200.

Substituting x = 200 back: selling price at 5% gain = Rs. 210, selling price at 5% loss = Rs. 190, and their difference is Rs. 210 − Rs. 190 = Rs. 20, confirming the cost price is Rs. 200.