Bunuel wrote:

The price of a shirt 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%

Method 2:

The second method is similar to the first one, but instead of using a formula, we will solve it by assuming the original price to P and applying the discounts on it.

Original Price : P

Price after first discount \(= P ( 1 - \frac{F}{100})\) , where F is the first discount.

Price after the second discount \(= P ( 1 - \frac{F}{100}) ( 1 - \frac{25}{100}) = \frac{3P}{4} * ( 1 - \frac{F}{100})\) ......(i)

According to the question stem, the two successive discount is equivalent to one discount of 40%.

Thus, price after overall discount can be written as \(P ( 1 - \frac{40}{100}) = \frac{3P}{5}\) ........(ii)

Equating equation (i) and (ii), we will get

\(\frac{3P}{4} * (1 - \frac{F}{100}) = \frac{3P}{5}\)

\(5 - \frac{5F}{100} = 4\)

\(\frac{F}{20} = 1\)

\(F = 20\)%

Thus, the correct answer is

Option C.

_________________

Ace GMAT quant

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