If a merchant makes a profit of 20% based on the selling...

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

If a merchant makes a profit of 20% based on the selling...

by BTGmoderatorLU » Fri Feb 23, 2018 2:33 pm

If a merchant makes a profit of 20% based on the selling price of an article, what percent does the merchant makes on the cost?

A. 20
B. 40
C. 25
D. None of these

The OA is C.

I'm confused by this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Fri Feb 23, 2018 2:33 pm

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Sat Feb 24, 2018 2:13 am

Hello LUANDATO.

We have to look at this question carefully.

Let's say that the selling price is $100.

Then, 20% profit means that the cost price is $80 and $20 is the profit obtained.

Now we need to find what percent of $80 represents $20:

$80--------------100%
$20---------------x%

Therefore, $$x=\frac{20\cdot100}{80}=\frac{200}{8}=25\%.$$ Hence, the merchant made a 25% on the cost price.

This implies that the correct answer is C.

I hope it helps you.

Feel free to ask me again if you have a doubt.

Regards.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Jun 14, 2019 2:45 pm

BTGmoderatorLU wrote:If a merchant makes a profit of 20% based on the selling price of an article, what percent does the merchant makes on the cost?

A. 20
B. 40
C. 25
D. None of these

We can let R = selling price and C = cost and create the equation:

R - C = 0.2R

0.8R = C

In terms of R, we see that the profit is 0.2R and the cost is 0.8R. Thus the profit as a percent of cost is:

0.2R/0.8R = 0.2/0.8 = 2/8 = 1/4 = 25%

Alternate Solution:

Let's assume the selling price is $100 and let c = the cost of the item. We know that selling price - cost = profit, or:

100 - c = 100 x 0.2

100 - c = 20

80 = c

Since the cost of the item is $80 and the profit made on its sale is $20, we see that the profit as a percent of cost is 20/80 = 1/4 = 25%.

Answer: C

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