Three successive discounts on the marked price of an article are equivalent to a single discount of 31.6%. If the first and second discounts are 10% and 5% respectively, what is the third discount?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20%
Successive discounts multiply: each leaves a fraction of the price, and the three fractions together leave what the single discount leaves.
Single discount 31.6% leaves \(0.684\) of the price
First two leave \(0.9\times0.95=0.855\)
Third leaves \(0.684\div0.855=0.8\), so the third discount is 20%
The third discount is 20%.
Why the other options are incorrect
Option (1) 25% — Incorrect. Discounts of 10%, 5% and 25% leave \(0.64125\) of the price, a single discount of 35.875%, not 31.6%.
Option (3) 16.6% — Incorrect. Discounts of 10%, 5% and 16.6% leave \(0.71307\) of the price, a single discount of 28.693%, not 31.6%.
Option (4) 15% — Incorrect. Discounts of 10%, 5% and 15% leave \(0.72675\) of the price, a single discount of 27.325%, not 31.6%.