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

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A car dealership orders 80 automobiles from the factory and wants to [#permalink]

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New post 17 May 2017, 23:15
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Question Stats:

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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
[Reveal] Spoiler: OA

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Re: A car dealership orders 80 automobiles from the factory and wants to [#permalink]

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New post 18 May 2017, 03:35
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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

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Re: A car dealership orders 80 automobiles from the factory and wants to [#permalink]

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New post 18 May 2017, 03:46
Bunuel wrote:
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



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

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Re: A car dealership orders 80 automobiles from the factory and wants to [#permalink]

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New post 18 May 2017, 04:41
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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 SP

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 or 400

It is 400/8000*100 or 5%(Option E)

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Re: A car dealership orders 80 automobiles from the factory and wants to [#permalink]

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New post 18 May 2017, 04:48
Bunuel wrote:
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


$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.
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Re: A car dealership orders 80 automobiles from the factory and wants to [#permalink]

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New post 22 May 2017, 17:27
Bunuel wrote:
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


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
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A car dealership orders 80 automobiles from the factory and wants to [#permalink]

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New post 20 Nov 2017, 19:19
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

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A car dealership orders 80 automobiles from the factory and wants to   [#permalink] 20 Nov 2017, 19:19
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