Find a single discount equivalent to a series discount of 20%, 10% and 5%.
2023
Find a single discount equivalent to a series discount of 20%, 10% and 5%.
Answer: B. 31.6% — CONCEPT Successive discounts act on the price remaining after each earlier discount, so their percentages cannot simply be added. For discounts d₁, d₂, …, the…
- A.
30%
- B.
31.6%
- C.
30.6%
- D.
32%
Show answer & explanation
Correct answer: B
CONCEPT
Successive discounts act on the price remaining after each earlier discount, so their percentages cannot simply be added.
For discounts d₁, d₂, …, the retained-price fraction is (1 − d₁)(1 − d₂)…, and the equivalent discount is 1 minus that product.
APPLICATION
Take the original price as 100.
After a 20% discount, the price is 100 × 0.80 = 80.
After the next 10% discount, the price is 80 × 0.90 = 72.
After the final 5% discount, the price is 72 × 0.95 = 68.4.
The total reduction is 100 − 68.4 = 31.6, which is 31.6% of the original price.
CROSS-CHECK
Using the retention-factor formula directly: 1 − (0.80 × 0.90 × 0.95) = 1 − 0.684 = 0.316 = 31.6%.
RESULT
The equivalent single discount is 31.6%.