Question : A single discount equivalent to three successive discounts of 8%, 15% and 12% is:
Option 1: 17.5%
Option 2: 68.816%
Option 3: 35%
Option 4: 31.184%
Correct Answer: 31.184%
Solution :
The successive discounts are 8%, 15% and 12%.
Let the initial value be 100.
Discounted value = (100 – 8)% of (100 – 15)% of (100 – 12)% of 100
= 92% of 85% of 88% of 100
= $\frac{92}{100} × \frac{85}{100} × \frac{88}{100} × 100$
= 68.816
Equivalent discount = $\frac{(100 - \text{Discounted value})}{\text{Initial value}} \times 100=\frac{(100 - 68.816)}{100} \times 100=31.184$%
Hence, the correct answer is 31.184%.
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