XAT 2018QA & DI Question 4

Successive Percentage ChangeEasy

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.

Answer & solution

  • A

    20

  • B

    25

  • C

    50

  • 100

  • E

    None of the above

Solution

Given, P(1+X100)(1-Y100) = P

(1+X100)(1-Y100) = 1   …(1)

⇒ X > Y
 
It is also given that X – Y = Y.

⇒ X = 2Y

Substituting this in (1)

(1+2Y100)(1-Y100) = 1

⇒ 1 -  (2Y210000 + Y100 = 1

⇒ Y = 50

∴ X = 100

Hence, option (d).

XAT 2018 QA & DI Q4: The price of a product is P. A shopkeeper raises its price by X% and then offers a discount of Y% on the raise — Solution | TheCATExam