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%
Let n denote the original price of the shirt and let the first discount be x percent. Then, after the first discount, the price is reduced to n(1 - x/100). After the second discount, the price is reduced to n(1 - x/100)(1 - 25/100) = n(1 - x/100)(75/100) = n(1 - x/100)(3/4).
Since the two discounts are equivalent to a single discount of 40 percent of the original price, we have:
n(1 - x/100)(3/4) = (60/100)n
(1 - x/100)(3/4) = 3/5
1 - x/100 = 4/5
x/100 = 1/5
x = 100/5 = 20
Answer: C
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