The successive discounts of 20% and 15% are equal to a single discount of

For two successive percentage discounts applied one after another, the second discount is taken off the price that has already been reduced by the first discount, not off the original price. If the first rate is r1% and the second is r2%, the single discount that has the same overall effect is r1 + r2 − (r1 × r2)/100 — equivalently, the fraction of the original price left after both discounts equals (1 − r1/100) × (1 − r2/100).

1. Take the original price as 100 (any convenient base works, since a percentage discount is scale-independent).

2. Apply the first 20% discount: the price becomes 100 × (1 − 20/100) = 100 × 0.80 = 80.

3. Apply the second 15% discount on this already-reduced price of 80 (not on the original 100): the price becomes 80 × (1 − 15/100) = 80 × 0.85 = 68.

4. The total amount removed from the original price is 100 − 68 = 32 out of 100, so the single discount that has the same effect as the two successive discounts is 32%.

Cross-check with the direct successive-discount formula: combined discount = r1 + r2 − (r1 × r2)/100 = 20 + 15 − (20 × 15)/100 = 35 − 3 = 32%, which matches the step-by-step computation above.