When the price of a pair of shoes is decreased by 10%, the number of pairs…

Concept: For two successive percentage changes of x% and y% applied to the same base quantity (here, price and the quantity sold, whose product gives total revenue), the net percentage change is not simply their sum. It is given by:

Net % change = x + y + (x × y) / 100

Here, a decrease is taken as negative and an increase as positive.

Application:

1. Let x = −10% (the 10% decrease in price) and y = +20% (the 20% increase in the number of pairs sold).

2. Net % change = x + y + (x × y)/100 = −10 + 20 + (−10 × 20)/100

3. = 10 + (−200/100) = 10 − 2 = 8

4. Since the result is positive, total sales revenue rises by 8%.

Cross-check:

Take the original price as P and the original number of pairs sold as N, so the original sales revenue is N × P. After the changes, the new price is 0.9P and the new number of pairs sold is 1.2N, so the new sales revenue is 1.2N × 0.9P = 1.08NP — exactly 8% more than NP, confirming the result above.

Result: The net effect on sales is an 8% increase.