A wholesaler offers a trade discount of 20% on the listed price of a machine.…

Concept — a discount is always charged on the price it is applied to, so two discounts given one after the other are multiplicative and never additive. For a listed price L with a first discount of a% and then a second discount of b% on the already-reduced price, the amount payable = L × (1 − a/100) × (1 − b/100). The same pair of discounts equals one single discount of (a + b − ab/100)% on the listed price.

Application — here the machine is listed at ₹10,000, the wholesaler gives a trade discount of 20%, and a cash discount of 5% is then allowed on the reduced price.

1. Trade-discount stage: price after 20% off the listed price = 10,000 × (1 − 20/100) = 10,000 × 0.80 = ₹8,000.

2. Base of the cash discount: the 5% is allowed on the reduced price, so it is charged on ₹8,000 and not on the ₹10,000 listed price.

3. Cash discount = (5/100) × 8,000 = ₹400.

4. Amount finally paid = 8,000 − 400 = ₹7,600.

Cross-check — by the single-equivalent-discount form, 20 + 5 − (20 × 5)/100 = 24%, so the amount payable = 10,000 × (1 − 24/100) = 10,000 × 0.76 = ₹7,600 — the same figure reached by an independent route.

Contrast — adding the two rates as 20% + 5% = 25% would give 10,000 × 0.75 = ₹7,500. That shortcut fails because the second discount is charged on the already-reduced price, which is smaller than the listed price, so the multiplicative form is what keeps the base of the second discount correct.