Question

The price of a product is P. A shopkeeper raises its price by X% and then offers a discount of Y% on the raised price. The discounted price again becomes P. If Y is the difference between X and Y, then find X.

Accepted Answer

D. Given $Y = X - Y \implies X = 2Y$. Net change: $\left(1 + \frac{X}{100}\right)\left(1 - \frac{Y}{100}\right) = 1 \implies \left(1 + \frac{2Y}{100}\right)\left(1 - \frac{Y}{100}\right) = 1$. $1 + \frac{Y}{100} - \frac{2Y^2}{10000} = 1 \implies \frac{Y}{100} = \frac{2Y^2}{10000} \implies Y = 50$. Therefore, $X = 2Y = 100$.

Percentage Changes and Net Effect

Explanation

Practise this under exam conditions