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

Question

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.

B.

C.

D.

E.

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

EgmatQuantExpert · Accepted Answer

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

vaibhav1221 · Answer

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%

chetan2u · Answer

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

hibobotamuss · Answer

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?

vaibhav1221 · Answer

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

EMPOWERgmatRichC · Answer

Hi All,

We're told that a newly-opened retail store made $400 profit on the initial expenditure of $25000, and then made $1200 profit on the next $80000 expenditure. We're asked for the approximate percentage change in the ratio of profit to expenditure change from the first $25000 expenditure to the next $80000 expenditure. This question requires the use of the Percentage Change Formula - and you will likely find it helpful to rewrite the given values as individual percentages (instead of fractions).

Percentage Change = (New - Old)/(Old) = Difference/Original

The ratio of the original profit-to-expenditure = 400/25000 = 4/250 
The ratio of the second profit-to-expenditure = 1200/80000 = 12/800

We can rewrite those fractions as percents... 
4/250 = 16/1000 = 1.6% 
12/800 = 1.5/100 = 1.5%

Thus, there was clearly a decrease (from 1.6% to 1.5%). Using the Percentage Change Formula, we have...

(1.6 - 1.5)/(1.6) = 0.1/1.6 = 1/16 = a 6 1/4% decrease.

Final Answer:  B

GMAT assassins aren't born, they're made, 
Rich

babji777 · Answer

Initial profit is $400 on initial investment $ 25000 
 Profit percentage = 400/25000 *100=16%
Second time profit is $1200 on second investment at $80000
Second time profit percentage=
1200/80000*100=15%
 Differential profit % is = final -initial/ initial
 (15-16)/16= -1/6 =-6.25 decrease.

Posted from my mobile device

nikitathegreat · Answer

Why did we not divide by expenditure since the question asked for profit/expenditure? We have taken out the profit if the expenditure is 80,000 in both the scenarios and then used only profit as a metric to understand the change? Can you please help me understand this. 
Thanks 
 GMATNinja   karishma

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

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