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The price of a dress was first discounted by a certain percent and lat 13 Jun 2017, 05:55
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81% (01:56) correct 19% (02:42) wrong based on 702 sessions

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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%
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C
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The price of a dress was first discounted by a certain percent and lat 13 Jun 2017, 06:38
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Bunuel
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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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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The price of a dress was first discounted by a certain percent and lat 13 Jun 2017, 06:30
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Bunuel
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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(1-x/100)*0.75 = 0.6

x = 20

Answer: option C
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The price of a dress was first discounted by a certain percent and lat 15 Jun 2017, 16:15
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Bunuel
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%
Show more

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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The price of a dress was first discounted by a certain percent and lat 29 Dec 2017, 19:25
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Bunuel
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%
Show more


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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The price of a dress was first discounted by a certain percent and lat 30 Dec 2017, 00:36
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Bunuel
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%
Show more

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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Bunuel
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%
Show more

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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The price of a dress was first discounted by a certain percent and lat 04 Nov 2020, 01:34
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Let P be the original price and 'x' be the first discount.

Price - discount = Selling price.[25% discount: 100 - 25 = 75% S.P. and 40% discount: 100 - 40 = 60% S.P. ]

\(P * \frac{(100-x)}{100} * \frac{75 }{ 100} = P * \frac{60}{100}\)

=> (100 - x) * \(\frac{3}{4}\) = 60

=> 3(100 - x) = 240

=> 300 - 3x = 240

=> 60 = 3x

=> x = 20

Answer C
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The price of a dress was first discounted by a certain percent and lat 27 Nov 2024, 00:04
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Bunuel
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%
Show more

Say bro bought a dress at 100 bucks, and they had it on like x% discount and cause of black friday he got another 25% discount over that discounted price, and then like when he saw he kinda figured it was like 40% discounted in total

so we gotta plug the prices after the discount, not the discount value

100*x/100 = $x discount = price of the product would be $100 - $x

on this he got 25% discount, so the price would be ($100 - $x)*75/100

and just to compare it with the overall 40% bro thought he got, now lets see

($100 - $x)*75/100 = 100 - (40*100/100)


($100 - $x)*3/4= 60

X= 100 - 80 = $20

so x% is like 20%, so bro got like 20% discount first and another 25% discount over that 20% which would make that product 60% of its value or 40% discounted
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