On an Rs. 10,000 payment order, a person has a choice between 3 successive…

Concept: When a price is cut by several successive discounts, each discount applies to the amount left after the previous discount — not to the original price, and the percentages are never simply added together. So a sequence of discounts d1, d2, d3 (as fractions) brings the price down to the original amount × (1 − d1) × (1 − d2) × (1 − d3). To compare two such discount sequences, work out the final price under each and see which is lower — that sequence is the better one. The amount saved by choosing the better sequence over the other is the difference between the two final prices.

Application on this Rs. 10,000 order:

1. First sequence (10%, 10%, 30%): Rs. 10,000 × 0.90 = Rs. 9,000 after the first discount.

2. Rs. 9,000 × 0.90 = Rs. 8,100 after the second discount.

3. Rs. 8,100 × 0.70 = Rs. 5,670 after the third discount, so the final price under the first sequence is Rs. 5,670.

4. Second sequence (40%, 5%, 5%): Rs. 10,000 × 0.60 = Rs. 6,000 after the first discount.

5. Rs. 6,000 × 0.95 = Rs. 5,700 after the second discount.

6. Rs. 5,700 × 0.95 = Rs. 5,415 after the third discount, so the final price under the second sequence is Rs. 5,415.

Since Rs. 5,415 is lower than Rs. 5,670, the second sequence (40%, 5%, 5%) is the better choice. The amount saved by choosing it over the first sequence is Rs. 5,670 − Rs. 5,415 = Rs. 255.

Cross-check: the first sequence alone saves Rs. 10,000 − Rs. 5,670 = Rs. 4,330 against the original order value, and the second sequence alone saves Rs. 10,000 − Rs. 5,415 = Rs. 4,585 against the original order value. The extra amount gained by picking the second sequence over the first is Rs. 4,585 − Rs. 4,330 = Rs. 255, which matches the direct final-price difference above.