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

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

$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.

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:

[(1,732,000 - 1,650,000)/1,650,000] x 100 = (82,000/1,650,000) x 100 = 0.05 x 100 = 5%.

Answer: E

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

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

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

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

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

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