If a shopkeeper reduces the selling price of a fan from ₹ 800 to ₹ 780, his…

Loss percentage is always calculated relative to the cost price (CP): Loss% = ((CP − SP) / CP) × 100. For a fixed cost price, lowering the selling price raises the rupee loss while CP (the denominator) stays the same, so the loss percentage also rises.

1. Let the cost price of the fan be ₹x.

2. Loss percentage when the selling price is ₹800: Loss%1 = ((x − 800) / x) × 100.

3. Loss percentage when the selling price is ₹780: Loss%2 = ((x − 780) / x) × 100.

4. The problem states the loss percentage rises by 2, so Loss%2 − Loss%1 = 2, i.e. [(x − 780) − (x − 800)] / x × 100 = 2.

5. The numerator simplifies to a constant: (x − 780) − (x − 800) = 20, so (20 / x) × 100 = 2.

6. Solving 2000 / x = 2 gives x = 1000.

Check with x = ₹1000: at SP = ₹800, loss = ₹200, i.e. 20%; at SP = ₹780, loss = ₹220, i.e. 22%. The loss percentage moves from 20% to 22%, a rise of exactly 2 percentage points, which matches the condition given in the problem.

So the cost price of the fan is ₹1000.