Question : A single discount equivalent to three successive discounts of 6%, 15% and 14% is:
Option 1: 17.5%
Option 2: 31.286%
Option 3: 68.714%
Option 4: 34.357%
Correct Answer: 31.286%
Solution :
Let the marked price of the article be 100.
For three successive discounts of 6%, 15% and 14%,
Selling price = $\frac{100-\text{Discount}_1\%}{100}× \frac{100-\text{Discount}_2\%}{100}×\frac{100-\text{Discount}_1\%}{100}×$ marked price
⇒ Selling price = $\frac{100-6}{100}×\frac{100-15}{100}×\frac{100-14}{100}×100$
⇒ Selling price = $\frac{94}{100}×\frac{85}{100}×\frac{86}{100}×100$
⇒ Selling price = $68.714$
Now,
⇒ Discount percentage = $\frac{100 -68.714}{100}×100=\frac{38.286}{100}×100 = 31.286\%$
Hence, the correct answer is 31.286%.
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