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A certain radio costs a merchant $72. At what price must the merchant

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Bunuel
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A certain radio costs a merchant $72. At what price must the merchant [#permalink] New post   27 Feb 2018, 23:50
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A certain radio costs a merchant $72. At what price must the merchant sell this radio in order to make a profit of 20%?

(A) $86.40

(B) $92

(C) $90

(D) $144

(E) $148
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Re: A certain radio costs a merchant $72. At what price must the merchant [#permalink] New post   28 Feb 2018, 00:28
Bunuel wrote:
A certain radio costs a merchant $72. At what price must the merchant sell this radio in order to make a profit of 20%?

(A) $86.40

(B) $92

(C) $90

(D) $144

(E) $148


If the radio costs the merchant $72, in order to make a profit of 20%,

the merchant would have to sell the radio at 1.2*$72 = $86.40

Therefore, the merchant must sell the radio at $86.40(Option A) to make a profit of 20%
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Re: A certain radio costs a merchant $72. At what price must the merchant [#permalink] New post   28 Feb 2018, 11:30
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Solution



We are given:

    • Profit= 20% of cost price
    • Cost= $72

We need to find:

    • Selling price such that merchant makes a profit of 20%

We know,

    • Selling price= Cost price + profit
    • Selling price= Cost price+ 20% of cost price
    • Selling price= $72+20/100* $72
    • Selling price= $72+ 0.2* $72
    • Selling price= $72+$14.40
    • Selling Price= $86.40

Answer: A
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Re: A certain radio costs a merchant $72. At what price must the merchant [#permalink] New post   01 Mar 2018, 18:34
Expert Reply
Bunuel wrote:
A certain radio costs a merchant $72. At what price must the merchant sell this radio in order to make a profit of 20%?

(A) $86.40

(B) $92

(C) $90

(D) $144

(E) $148


We can let R = revenue and create the equation:

R - 72 = 0.2(72)

R - 72 = 14.4

R = 86.4

Answer: A
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Re: A certain radio costs a merchant $72. At what price must the merchant [#permalink] New post   22 Jun 2019, 21:54
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Profit%= 20%
C.P.=$72
Profit= Profit% of C.P.
= 20/100 * 72
= $14.40
S.P. = C.P. + Profit
= 72 + 14.40
= $86.40
Hence Option(A)
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Re: A certain radio costs a merchant $72. At what price must the merchant [#permalink] New post   22 Jun 2019, 22:44
It seems like a very simple question. Then, the idea should be how quickly one solves this.

Selling price = Cost price + Profit = \(72 + \frac{20}{100} = 72 + \frac{1}{5}\)

Looking at the numbers, we can see we will get a decimal answer if we go through with the calculation. A quick peek at the options show that only option A has decimal. So that should be the answer.

Is this one of the right approaches to save few precious seconds?
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A certain radio costs a merchant $72. At what price must the merchant [#permalink] New post   16 Jul 2022, 23:04
We can solve this question by using logic and benchmarks -

Cost of the Radio - $72

Using benchmarks to solve this problem -

$72 = 100%

We need to sell the product at 120% of the original cost.

Divide by 10 on both sides to find 10 % of 72

7.2 = 10%

So, 10% + 10% = 7.2 + 7.2 i.e 14.4

Add this 20% to the original $72

72 + 14.4 = 86.4 i.e ANSWER A

We can eliminate a few answers at the start by reasoning out the following - A quick glance at the answers reveals all of 'em to be higher than $72, but the answers are far apart. For example - Answers C & D are double i.e 200% of $72, and we need 20% of $72
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A certain radio costs a merchant $72. At what price must the merchant [#permalink]
16 Jul 2022, 23:04
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