The difference between a discount of 40% on Rs 500 and two successive…

Concept: Successive percentage discounts combine multiplicatively, not by simple addition. Applying two discounts of d1% and d2% one after another leaves (1 − d1/100) × (1 − d2/100) of the original price — this is not the same as removing (d1 + d2)% in one shot, even when d1 + d2 happens to equal another quoted single discount percentage.

1. Price after a single 40% discount on Rs 500 = 500 × (1 − 0.40) = 500 × 0.60 = Rs 300.

2. Price after successive discounts of 36% and 4%: first apply 36% → 500 × 0.64 = Rs 320; then apply 4% to this reduced price → 320 × 0.96 = Rs 307.20.

3. Difference between the two final prices = Rs 307.20 − Rs 300 = Rs 7.20.

Cross-check: the two successive discounts together are equivalent to a single discount of 1 − (0.64 × 0.96) = 1 − 0.6144 = 0.3856, i.e. 38.56%. That is 1.44 percentage points short of 40%, and 1.44% of Rs 500 is Rs 7.20 — matching the difference found above.