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

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Math Expert
Joined: 02 Sep 2009
Posts: 44636
The price of a shirt was first discounted by a certain percent and lat [#permalink]

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13 Jun 2017, 05:55
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Difficulty:

15% (low)

Question Stats:

82% (01:18) correct 18% (01:55) wrong based on 76 sessions

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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%
[Reveal] Spoiler: OA

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

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13 Jun 2017, 06:30
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Expert's post
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

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

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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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15 Jun 2017, 16:15
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Expert's post
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

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Joined: 29 Jan 2017
Posts: 47
Re: The price of a shirt was first discounted by a certain percent and lat [#permalink]

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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

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

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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%

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Saquib
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Quant Expert
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Joined: 04 Jan 2015
Posts: 1010
Re: The price of a shirt was first discounted by a certain percent and lat [#permalink]

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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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Re: The price of a shirt was first discounted by a certain percent and lat   [#permalink] 30 Dec 2017, 00:44
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