Three successive discounts of 30% on the marked price of an item are together…
2024
Three successive discounts of 30% on the marked price of an item are together equivalent to a single discount of
Answer: C. 65.7% — Concept Discounts given one after the other multiply; they do not add. A discount of d% leaves (100 − d)% of whatever price it is applied to, so when…
- A.
90%
- B.
27%
- C.
65.7%
- D.
78.2%
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Show answer & explanation
Correct answer: C
Concept
Discounts given one after the other multiply; they do not add. A discount of d% leaves (100 − d)% of whatever price it is applied to, so when discounts are given in succession the fraction of the marked price that survives is the product of the surviving fractions, and the equivalent single discount is 100% minus that surviving fraction.
Application
Every discount here is 30%, so each stage leaves 70% of the price entering that stage: the multiplier per stage is 0.7.
Three such stages act in succession, so the surviving fraction of the marked price is 0.7 × 0.7 × 0.7 = 0.73 = 0.343.
A surviving fraction of 0.343 means 34.3% of the marked price is still payable.
The equivalent single discount is therefore 100% − 34.3% = 65.7%.
Cross-check
Take a marked price of ₹1,000 and apply the three discounts one at a time:
Stage | Price (₹) |
|---|---|
Marked price | 1,000 |
After the first 30% | 700 |
After the second 30% | 490 |
After the third 30% | 343 |
The total reduction is ₹1,000 − ₹343 = ₹657, which is 65.7% of the marked price. Read stagewise, the reductions are 30% + 21% + 14.7% = 65.7% — the same result.
Contrast
Adding the rates (30 + 30 + 30 = 90) overstates the reduction, because the second and third discounts act on a price that has already shrunk rather than on the full marked price. Multiplying the discount rates themselves (0.3 × 0.3 × 0.3 = 0.027) does not model successive discounts either — what must be multiplied is the surviving fractions (0.7), not the discount fractions (0.3).