A shopkeeper cheats to the extent of 10% while buying and selling, by using…

Concept: When a trader cheats by x% while buying and by y% while selling using a false weight, the two false-weight errors compound rather than simply add — the total gain works out to x + y + (xy)/100, not just x + y.

Working:

1. Here the cheating rate is the same in both transactions: x = y = 10%.

2. Total gain% = x + y + (xy)/100

3. Substitute the values: 10 + 10 + (10 × 10)/100

4. = 20 + 1 = 21%

Cross-check: Take a reference weight of 1000 g. While buying, the false weight lets the trader actually receive 1100 g (10% more) for the price of 1000 g. While selling, he claims to give 1000 g but actually hands over only 1000/1.1 ≈ 909.09 g (10% less). So the 1100 g he holds is sold off in units of 909.09 g, giving 1100/909.09 ≈ 1.21 such units — i.e. 21% more revenue than the cost, confirming the result above.

Answer: 21%.