Two shopkeepers A and B sell a certain kind of machine at the same list price.…
2022
Two shopkeepers A and B sell a certain kind of machine at the same list price. However, shopkeeper A allows two successive discounts of 20% and 15%, while shopkeeper B allows two successive discounts of 10% and 25%. Which of the following statements is correct?
Answer: B. 'B' offers more discount — ConceptFor two successive discounts of r% and s%, the retained-price factor is (1 - r/100)(1 - s/100). The effective discount is 1 minus this factor.…
- A.
'A' offers more discount
- B.
'B' offers more discount
- C.
Both 'A' and 'B' offer same discount
- D.
'A' offers 35% discount and 'B' offers 30% discount
Attempted by 3 students.
Show answer & explanation
Correct answer: B
Concept
For two successive discounts of r% and s%, the retained-price factor is (1 - r/100)(1 - s/100). The effective discount is 1 minus this factor.
Successive percentage discounts must be multiplied because the second discount acts on the already reduced price; simply adding the rates is generally invalid.
Application
Let the common list price be 100.
For A, the price after the discounts is 100 × 0.80 × 0.85 = 68, so A gives an effective discount of 100 - 68 = 32%.
For B, the price after the discounts is 100 × 0.90 × 0.75 = 67.5, so B gives an effective discount of 100 - 67.5 = 32.5%.
Because 32.5% is greater than 32%, B offers the larger effective discount.
Cross-check
Using d = r + s - rs/100 gives A: 20 + 15 - 3 = 32%, and B: 10 + 25 - 2.5 = 32.5%, confirming the comparison.
Result
Therefore, B offers more discount.