Question 75

If the price of an eraser is reduced by 25%, a person can buy three more erasers for ₹ 2. How many erasers can be bought for ₹ 2 as the original price?

Solution

Let the original price of 1 eraser = $$a$$

Number of erasers that can be bought for ₹2 = $$\frac{2}{a}$$

Price of 1 eraser when reduced by 25% = $$\frac{75}{100}a$$ = $$\frac{3}{4}a$$

Number of erasers that can be bought for ₹2 after reduction in price = $$\frac{2}{\frac{3}{4}a}$$ = $$\frac{8}{3a}$$

According to the problem,

$$\frac{2}{a}+3=\frac{8}{3a}$$

$$\Rightarrow$$  $$\frac{8}{3a}-\frac{2}{a}=3$$

$$\Rightarrow$$  $$\frac{2}{3a}=3$$

$$\Rightarrow$$  $$a=\frac{2}{9}$$

$$\therefore\ $$Number of erasers that be bought for ₹2 with original price = $$\frac{2}{a}$$ = $$\frac{2}{\frac{2}{9}}$$ = 9

Hence, the correct answer is Option C


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