A car dealership orders 80 automobiles from the factory and wants to

Question

A car dealership orders 80 automobiles from the factory and wants to sell each for $22,275. 60 of the cars are sold at this price, which represented an 8% profit above the dealership’s cost from the factory. To sell the remaining 20 cars, the dealership has to substantially discount the retail price, and each is sold at a price that represents a 4% loss below the dealership’s cost. What was the dealership’s profit or loss as a percent of the dealership’s initial cost for the 80 automobiles?

A. 5% loss
B. 4% loss
C. 2% profit
D. 4% profit
E. 5% profit

A. 5% loss
B. 4% loss
C. 2% profit
D. 4% profit
E. 5% profit

varundixitmro2512 · Accepted Answer

IMO E

Thought first solving it with conventional took me 5.5 minutes then I managed to get a shortcut

60*+8 =480
20*-4=-80

total=+400
per car 400/80 =+5

pushpitkc · Answer

I'd plug in a number, let say 100 as the CP of the cars.

Given data is 
60 sold at 8% more than CP
20 sold at 4% less than CP

Total CP:  80*100 = 8000 
Total SP:  60*1.08*100 + 20*.96*100 = 60*108 + 20*96 = 6480+1920 = 8400

Profit is SP - CP, which is  400(8400-8000) 
 
Therefore, the profit percentage is  \frac{400}{8000}*100  or  5%(Option E)

Rohit2015 · Answer

weighted avg. is rather much faster method for above such problems

Let x be avg. profit/loss

then

60/20= (-4-x)/x-8

3x-24= -4-x

4x = 20

x=5

ans E

broall · Answer

$22,275 represented 8% profit, so the cost is $\frac{22,275}{1.08}=20,625$

Sell remaining 20 cars at price: $20,625 \times 0.96 = 19,800$

The total revenue: $60 \times 22,275 + 20 \times 19,800$
The total cost: $80 \times 20,625$

The profit/loss ratio: $\frac{(60 \times 22,275 + 20 \times 19,800) - 80 \times 20,625}{80 \times 20,625}$
$=\frac{6 \times 22,275 + 2 \times 19,800}{8 \times 20,625} - 1 \
= \frac{3 \times 22,275 + 19,800}{4 \times 20,625} - 1 \
= 1.05 - 1 = 0.05 = 5 \%$

The answer is E.

ScottTargetTestPrep · Answer

We are given that 60 cars were sold for $22,275 at a profit of 8%. Thus:

Profit = 0.08(cost)

Revenue - cost = 0.08(cost)

22,275 - c = 0.08c

22,275 = 1.08c

22,275/1.08 = c

20,625 = c

Thus, the dealership’s cost for each car was 20,625 dollars.

We are also given that 20 cars were sold at a loss of 4%. Thus, each of the remaining 20 cars was sold at 96% of the dealership’s cost.

Thus, each of the remaining 20 cars was sold for 0.96(20,625) = $19,800.

In total, the dealership spent 20,625 x 80 = 1,650,000 on the cars and earned:

22,275 x 60 + 19,800 x 20 = 1,336,500 + 396,000 = 1,732,500

Thus, the dealership made a profit on the sale of 80 cars and the profit is:

x 100 = (82,000/1,650,000) x 100 = 0.05 x 100 = 5%.

Answer: E

hellosanthosh2k2 · Answer

Can be solved quickly using weighted average concept.

96 (4% loss, 20 cars(weightage) ) <------------------------------------------> 108 (8% profit, 60 cars (weightage))

60:20 = 3 : 1

96 <--------------3------------------->|<--------1-------->108

so the diff between 108 - 96 , must be divided in 3:1 ratio (60:20) according to weightage
so weighted average = $96 + (12 * 3/4) = 105$ = 5% profit, Answer (E)

Thanks

HimanshuW11 · Answer

The awkward numbers in this problem and the seemingly tedious calculations required to solve it are a hint to look for a faster approach. While you could calculate the total profit on the 60 cars and the total loss on the 20 cars, combine, and divide by the total cost to the dealership, this would take a very, very long time Since the problem is about percentage profit or loss, the values of the cars are not important. The answer will be the same if it is a $10,000 car, a $15,000 car or a $22,275 car. This is really just a good old-fashioned weighted average problem. ¾ of the cars were sold at an 8% profit and ¼ were sold at a 4% loss. This means the ratio of cars with a profit to cars with a loss is 3:1 and this controls the weighting between +8% and -4%. Using the mapping strategy, see that the combined profit would be 5%:

-4% ------------------------------5%-------8%
----------------9%----------------------3%-----
The ratio of 8% profit to 4% loss is the correct 3:1.

Veritas Prep Solution

-4% ------------------------------5%-------8% 
----------------9%----------------------3%-----
The ratio of 8% profit to 4% loss is the correct 3:1.

Veritas Prep Solution

rZAhyYJtj · Answer

I just did 8*(3/4) + (-4)*(1/4) = 6 - 1 = +5%.

MathRevolution · Answer

Le the C.P. of 1 car is 100.

Total C.P.: 80 * 100 = 8,000

Total S.P.: 60 cars with 8% profit and 20 cars with a 4% loss

=> 60 *  \frac{108}{100}  * 100 + 20 *  \frac{96}{100}  * 100

=> 6480 + 1920

=> 8,400

Overall Profit: S.P. - C.P.

=> 8,400 - 8,000 = 400

Profit percentage:  \frac{400 }{ 8000}  * 100 = 5%

Answer E

Kritisood · Answer

the weight of the car sold at profit and loss is 60:20 =>3:1

\frac{108(3)+96(1)}{4} = 105  hence 5% profit

GMATBusters · Answer

The best way to solve this ques is using weighted average.

{8*60+(-4)*20}/80 =5

E. 5% Profit

EnglishAgast · Answer

Hi  Bunuel

Are there more such questions like this where we can practice and solve using weighted averages method?

Bunuel · Answer

You can use the search box in the PS forum to find similar questions by entering key words like profit , loss , and cost . https://gmatclub.com/forum/download/file.php?id=82983 Here is a result: search.php?keywords=profit+lost+cost&terms=all&fid%5B%5D=140&author=&sc=1&sk=re&sd=d&d_s=1&sf=all&sr=posts&sj=one&t=0&submit=Search GMAT-Club-Forum-57r2lvy9.png

EnglishAgast · Answer

Understood, thank you Bunuel! GMAT-Club-Forum-wulr77tl.png

IcanDoIt23 · Answer

Here the absurd number (22,275) given as price is of no use. See below why:

The question asks us to find the overall profit or loss after selling 80 cars,   as a percentage of initial cost of 80 cars  .

Since we are given a relation in Cost and 22,275 i.e., by telling 8% profit above cost = 22,275. We don't need to put this in the expression to find 60 cars revenue i.e., instead of writing  , we can say

Therefore, the overall expression becomes

+

divided by

Cost cancels out in numerator and denominator

Hence: the expression becomes: 60*1.08 + 20*0.96 / 80 = 1.05 => 5 percent profit

A car dealership orders 80 automobiles from the factory and wants to

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GMAT Problem Solving (PS) Questions

A car dealership orders 80 automobiles from the factory and wants to

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