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The price of a shirt was first discounted by a certain percent and lat

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The price of a shirt was first discounted by a certain percent and lat  [#permalink]

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New post 13 Jun 2017, 05:55
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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%

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Re: The price of a shirt was first discounted by a certain percent and lat  [#permalink]

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New post 13 Jun 2017, 06:30
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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%


(1-x/100)*0.75 = 0.6

x = 20

Answer: option C
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The price of a shirt was first discounted by a certain percent and lat  [#permalink]

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New post 13 Jun 2017, 06:38
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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 the price of article be = $100
Given Final selling price is 40% discount on the original price; ie; 60% of 100 \(= \frac{60}{100} * 100 = 60\)
Let the first discount be x%. Second discount is 25% on first discounted price. ie; 75% on first discount price.

If successive discounts of x% and y% are given on article P; Selling price of article after successive discounts = (100 - y) % of (100 - x)% of P
\(60 = (\frac{100 - 25}{100}) * (\frac{100 - x}{100}) * 100\)
\(60 = \frac{75}{100} * (100 - x)\)
\(60 = \frac{3}{4}(100 - x)\)
\(100 - x = 80\)
\(x = 100 - 80 = 20%.\) Answer C...
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Re: The price of a shirt was first discounted by a certain percent and lat  [#permalink]

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New post 15 Jun 2017, 16:15
1
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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Re: The price of a shirt was first discounted by a certain percent and lat  [#permalink]

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New post 29 Dec 2017, 19:25
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%



Working backwards/picking numbers was the easiest for me.

100 - 40% = 60

We need an answer choice that matches 60

D) 100 - 30% = 70
This part is the second discount (25%): 70 x (3/4) does not = 60

C) 100 - 20% = 80
80 x (3/4) = 60

C is the answer
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Re: The price of a shirt was first discounted by a certain percent and lat  [#permalink]

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New post 30 Dec 2017, 00:36
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%


There are a number of ways to solve this question. Let me start with the smallest one. :)

Method 1:



We can use the percentage formula to get the first discount.

\(A + B + \frac{(A * B)}{100}\) = Overall Percentage.

A is unknown, B = -25 and Overall Percentage Discount = -40 [Note : We are using a negative sign, since these percentages are discounts]

Plugging in the numbers in the above formula we get :

\(A - 25 + A * \frac{(-25)}{100} = -40\)

\(A - \frac{A}{4} = - 15\)

\(A = - 15 * \frac{4}{3}\)

\(A = - 20\)

Thus the first discount = 20%

Correct answer is Option C.


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Re: The price of a shirt was first discounted by a certain percent and lat  [#permalink]

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New post 30 Dec 2017, 00:44
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.
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