Profit and loss

Question

Q.1 A man buys 2 dozen bananas at $16 per dozen. After selling 18 bananas at the rate of $12 per dozen, the shopkeeper reduced the rate to $4 per dozen. The % loss is A 25.2 B 34.2 C 36.5 D 37.5 E 40

Jay@ManhattanReview · Answer

Hi vaibhav101,

Pl. post each of the three questions as a separate post.

-Jay
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Rich.C@EMPOWERgmat.com · Answer

Hi vaibhav101,

A 'dozen' is 12, so since this question organizes all of its information in terms of 'dozens', you can either focus on that unit of measure or work on a 'per banana' calculation. Here's how you can focus on dozens of bananas at a time:

We're told that 2 dozen bananas are purchased for $16/dozen. That's a cost of...
(2)($16) = $32 to purchase the 2 dozen bananas

Then we're told the prices that the bananas were sold for:
18 bananas = 1.5 dozen at $12/dozen = (1.5)($12) = $18
6 bananas = 1/2 dozen at $4/dozen = (.5)($4) = $2
Total revenue = $18 + $2 = $20

The question asks for "% loss", which implies the percent change in revenue relative to cost.

(Revenue - Cost)/(Cost) = (20 - 32)/32 = -12/32 = - 3/8 = -37.5%

Final Answer: D

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Rich

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DavidG@VeritasPrep · Answer

vaibhav101 wrote:Q.1 A man buys 2 dozen bananas at $16 per dozen. After selling 18 bananas at the rate of $12 per dozen, the shopkeeper reduced the rate to $4 per dozen. The % loss is
A 25.2
B 34.2
C 36.5
D 37.5
E 40

You can also treat this as a weighted average.

Loss on bananas bought for $16/dozen and sold for $12/dozen = (16-12)/16 = 25%
Loss on bananas bought for $16/dozen and sold for $4/dozen = (16-4)/16 = 75%

18 bananas were sold at $12/dozen and the remaining 6 were sold at $4/dozen. So there were three times as many bananas sold at a 25% loss than at a 75% loss. Call the distance between each loss and the average loss, 'x' and '3x.'

25---------Average Loss------------------75
Gap: x----------------------------3x---------

Distance from 25 to 75 = 50. x + 3x = 4x.
4x = 50 and x = 12.5

25 + 12.5 = 37.5. The answer is D

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Matt@VeritasPrep · Answer

He paid 2 * $16, or $32. He got back 1.5 * $12 + 0.5 * $4, or $20. He ended up with 20/32, or 5/8 of what he started with, meaning that he lost 3/8, or 37.5%.

Jeff@TargetTestPrep · Answer

vaibhav101 wrote:Q.1 A man buys 2 dozen bananas at $16 per dozen. After selling 18 bananas at the rate of $12 per dozen, the shopkeeper reduced the rate to $4 per dozen. The % loss is
A 25.2
B 34.2
C 36.5
D 37.5
E 40

You can also treat this as a weighted average.

Loss on bananas bought for $16/dozen and sold for $12/dozen = (16-12)/16 = 25%
Loss on bananas bought for $16/dozen and sold for $4/dozen = (16-4)/16 = 75%

18 bananas were sold at $12/dozen and the remaining 6 were sold at $4/dozen. So there were three times as many bananas sold at a 25% loss than at a 75% loss. Call the distance between each loss and the average loss, 'x' and '3x.'

25---------Average Loss------------------75
Gap: x----------------------------3x---------

Distance from 25 to 75 = 50. x + 3x = 4x.
4x = 50 and x = 12.5

25 + 12.5 = 37.5. The answer is D

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