Percentages - PS Set 40 Q11

[gmatrant]

The price of a dress was first discounted by a certain percent and later by 25 percent of the discounted price. If these two discounts are equivalent to a single discount of 40 percent of the original price, what was the first discount ?
(A) 10%
(B) 15%
(C) 20%
(D) 30%
(E) 65%

Can you let me know how to solve this?

[Suyog]

Let the Price of dress be 100

Now the Single Discount of 40, So the price of the dress will be 60.

We want to come to this value of 60 after an unknown discount and 25 percent discount.

Randomly i started with 20% discount ( 3rd Option.

20% of 100 gives 80

Now another discount of 25% on 80, which gives me 60...got it!

Ans C.

[mehadi.gani]

Let, The first discount = x%
and Original price = 100.
Then after deducting first discounts, the price becomes = (100-x)

Deducting the second discounts 25%, the price becomes =
(100-x)*(75/100) which is equal to the original price minus the single discount.

So, (100-x)*(75/100)=60
x=20 %