Question : The marked price of a cap is INR 2,000. Two successive discounts of 15% and $x$% are given. If the selling price is INR 1,275, then what is the value of $x$?
Option 1: 20%
Option 2: 22.5%
Option 3: 27.5%
Option 4: 25%
Correct Answer: 25%
Solution :
Given,
The marked price of a cap is INR 2,000. Two successive discounts of 15% and $x$% are given and the selling price is INR 1,275.
We know,
Discounted price = $\frac{100-\text{discount percentage}}{100}×$ marked price
With successive discounts of 15% and $x$% in 2000,
⇒ $1275=\frac{100−15}{100}×\frac{100−x}{100}×2000$
⇒ $1275=\frac{85}{100}×\frac{100-x}{100}×2000$
⇒ $1275=\frac{85\times 2(100-x)}{10}$
⇒ $1275=17(100-x)$
⇒ $75=100-x$
⇒ $x=25$%
Hence, the correct answer is 25%.
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