[GMAT math practice question]

If the gross profit of a certain company is 20 percent of the revenue from sales of the company, what percent of the cost is the gross profit?

A. 20%
B. 25%
C. 30%
D. 35%
E. 40%
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Method 1: Profit (\(P\)) \(=\) Sales price (\(S\)) \(-\) Cost price (\(C\))

Given, Profit \((P)\) is \(20\)% of Revenue from sales (ie; sales price) \(= \frac{20}{100}*S = \frac{1}{5}S\)

Substituting value of \(P\) in Profit equation we get;

\(\frac{1}{5}S = S - C\)

\(C = S - \frac{1}{5}S = \frac{5S-1S}{5} = \frac{4}{5}S\)
Required Percentage \(= (\frac{P}{C}) * 100 = (\frac{\frac{1}{5}S}{\frac{4}{5}S}) * 100 = \frac{100}{4} = 25\)%

Method 2: Profit (\(P\)) \(=\) Sales price (\(S\)) \(-\) Cost price (\(C\))

Let \(S = 100\)

Given \(P\) is \(20\)% of \(S = \frac{20}{100} * 100 = 20\)

\(P = S - C\)

\(20 = 100 - C\)

\(C = 100 - 20 = 80\)

Required percentage \(= (\frac{P}{C}) * 100 = \frac{20}{80} * 100 = \frac{100}{4} = 25\)%

Answer (B)...

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=>
Let R be the revenue of the company. The profit is 0.2*R and the cost is 0.8*R.
The answer is (0.2*R) / (0.8*R) * 100 = 0.25 * 100 = 25(%).

Ans: B
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Let Profit P, revenue R and Cost C
So as Profit= Revenue -Cost
P=R-C

Given P= 20% of R = 20/100 * R =R/5 => R=5P

Putting in above equation => P =5P-C => C=4P => P=C/4
=> P= 25/100 * C
=> P = 25% of C

Answer: B

It helps to know
Revenue 100%
less: cost 80%
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Gross Profit 20%

Question what is Gross Profit as a % of cost = 20% /80% = 1/4 = 25%