Discussion

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.

Explanation:

Given, $P (1 + \frac{X}{100}) (1 - \frac{Y}{100})$ = P

⇒ $(1 + \frac{X}{100}) (1 - \frac{Y}{100})$ = 1 …(1)

⇒ X > Y

It is also given that X – Y = Y.

⇒ X = 2Y

Substituting this in (1)

⇒ $(1 + \frac{2 Y}{100}) (1 - \frac{Y}{100})$ = 1

⇒ 1 - ( $\frac{2 Y^{2}}{10000}$ + $\frac{Y}{100}$ = 1

⇒ Y = 50

∴ X = 100

Hence, option (d).

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