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A newly-opened retail store made $400 profit on the initial exp

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A newly-opened retail store made $400 profit on the initial exp  [#permalink]

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New post 26 Jul 2018, 00:41
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A newly-opened retail store made $400 profit on the initial expenditure of $25000, and then made $1200 profit on the next $80000 expenditure. By approximately what percent did the ratio of profit to expenditure change from the first $25000 expenditure to the next $80000 expenditure?

    A. 6.67% decrease
    B. 6.25% decrease
    C. 0
    D. 6.25% increase
    E. 6.67% increase

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Re: A newly-opened retail store made $400 profit on the initial exp  [#permalink]

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New post 26 Jul 2018, 01:00
\(25000*\frac{x}{100} = 400\)
\(x = \frac{8}{5}\)

\(80000*\frac{y}{100} = 1200\)
\(y = \frac{12}{8}\)

% change \(=\) \(\frac{New - Initial}{Initial}*100\)

\(\frac{\frac{12}{8} - \frac{8}{5}}{\frac{8}{5}}*100\)

=\(\frac{-1}{16}*100\)

= \(-6.25%\)
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Re: A newly-opened retail store made $400 profit on the initial exp  [#permalink]

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New post 26 Jul 2018, 01:08
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EgmatQuantExpert wrote:
A newly-opened retail store made $400 profit on the initial expenditure of $25000, and then made $1200 profit on the next $80000 expenditure. By approximately what percent did the ratio of profit to expenditure change from the first $25000 expenditure to the next $80000 expenditure?

    A. 6.67% decrease
    B. 6.25% decrease
    C. 0
    D. 6.25% increase
    E. 6.67% increase


Another way
let's see the profit on say 5000$

400 on 25000 so \(\frac{400}{5}=80\) in 5000
1200 on 80000 so \(\frac{1200}{(8*2)}=75\) in 5000
so profit decreased from 80 to 75, so change = \(\frac{(80-75)}{80}*100=\frac{500}{80}\)=6.25%

B
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Re: A newly-opened retail store made $400 profit on the initial exp  [#permalink]

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New post 27 Jul 2018, 01:50
Hi vaibhav1221 ...can you explain what exactly you've done?

Why haven't we just taken the differences of 2/125 and 200/3 and divided that by 2/125? Isn't that how you see percent change? :(
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Re: A newly-opened retail store made $400 profit on the initial exp  [#permalink]

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New post 27 Jul 2018, 02:50
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hibobotamuss wrote:
Hi vaibhav1221 ...can you explain what exactly you've done?

Why haven't we just taken the differences of 2/125 and 200/3 and divided that by 2/125? Isn't that how you see percent change? :(


Hi hibobotamuss!

See we need to compare the profits from both the expenditures.
We cannot simply compare $400 and $1200 to find the whether the profit has increased or decreased because the base value or the expenditure in both the situations is different. In order to solve this question, we can either make the base expenditure same as Chetan2u did or take the percentage markup or profit of the expenditure like I did.

So what i did was, I assumed that on an expenditure of $25000 the store made $400 i.e x% profit of 25000 and this is calculated as follows:-
\(25000*\frac{x}{100} = 400\)
\(x = \frac{8}{5}\)

I did the same thing for the other scenario wherein the expenditure was $80000 and profit was $1200 and this is calculated as follows:-
\(80000*\frac{y}{100} = 1200\)
\(y = \frac{12}{8}\)

I calculated the percentage markup on both the expenditures so that it gets a common base (percentage of something) and only then we can compare the two quantities.

Percentage change is measure as
% change \(=\) \(\frac{New - Initial}{Initial}*100\)

This is the formula to measure % change. Here the new value \(\frac{12}{8}\) and the initial value would be \(\frac{8}{5}\) because we need to find the percentage change from when the profit was $400 on an expenditure of $25000 to when the profit was $1200 on an expenditure of $80000.

I did the calculations as follows:-
\(\frac{\frac{12}{8} - \frac{8}{5}}{\frac{8}{5}}*100\)

=\(\frac{-1}{16}*100\)

= \(-6.25%\)

A negative answer implies a decrease.
So the answer is B.

Hope this helps.

Regards,
Vaibhav
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Re: A newly-opened retail store made $400 profit on the initial exp  [#permalink]

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New post 30 Jul 2018, 05:57
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Solution



Given:
    • A newly-opened retail store made $400 profit on the initial expenditure of $25000, and then made $1200 profit on the next $80000 expenditure

To find:
    • By approximately what percent did the ratio of profit to expenditure change from the first $25000 expenditure to the next $80000 expenditure

Approach and Working:
When the expenditure is $25000, the profit is $400

Maintaining the same ratio, we can say,
    • When the expenditure is $80000, the profit should be \(\frac{400}{25000} * 80000\) = $1280

However, on $80000 expenditure, the store is making a profit of $1200 only
    • Therefore, the percentage decrease in profit = \(\frac{1280 – 1200}{1280} * 100\) = 6.25%

Hence, the correct answer is option B.

Answer: B
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Re: A newly-opened retail store made $400 profit on the initial exp &nbs [#permalink] 30 Jul 2018, 05:57
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