Profit and loss

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vaibhav101: Master | Next Rank: 500 Posts; Posts: 138; Joined: Mon May 01, 2017 11:56 pm; Thanked: 4 times

by vaibhav101 » Sun Jun 04, 2017 10:05 pm

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

Last edited by vaibhav101 on Mon Jun 05, 2017 5:04 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Sun Jun 04, 2017 10:05 pm

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by Jay@ManhattanReview » Sun Jun 04, 2017 10:08 pm

Hi vaibhav101,

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

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by [email protected] » Mon Jun 05, 2017 10:30 am

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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DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Mon Jun 05, 2017 10:56 am

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: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Mon Jun 05, 2017 11:35 pm

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%.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue Jun 13, 2017 7:54 am

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

We are given that a man buys 2 dozen bananas for $16, so he pays $32.

He sells 18 bananas, or 1.5 dozen bananas, for $12 per dozen, so he receives a total of 1.5 x 12 = $18.

Since he reduces the price per dozen to $4, he receives from the sale of the remaining 0.5 dozen bananas 0.5 x 4 = $2.

Thus, he earns 18 + 2 = $20. His loss is 32 - 20 = $12 and the percentage loss is 12/32 = 3/8 = 37.5%.

Answer: D

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