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Problem solving : profit and loss

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by Jay@ManhattanReview » Sun Jun 04, 2017 4:58 am
vaibhav101 wrote:A trader mixes 26kg of rice at $20 per kg with 30kg of other variety at $36 per kg and sells the mixture at $30per kg. His profit % is
A zero
B 5
C 8
D 10
E -4
This question is based on the concept of weighted average. We must find out the weighted average price of the mixture.

Weighted average price = (Price of the first variety of rice*Price + Price of the second variety of rice*Price) / Total quantity

= (20*26 + 36*30) / (26+30) = 1600/56 = $200/7 per kg

Profit percent = [(Selling price - Weighted Average price) / Weighted Average price]*100%

= [(30 - 200/7) / (200/7)]*100% = [(210 - 200) / 200]*100% = 5%

The correct answer: B

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by GMATGuruNY » Sun Jun 04, 2017 6:57 am
vaibhav101 wrote:A trader mixes 26kg of rice at $20 per kg with 30kg of other variety at $36 per kg and sells the mixture at $30per kg. His profit % is
A zero
B 5
C 8
D 10
E -4
Total cost price for a mixture of 26 pounds of $20 rice and 30 pounds of $36 rice = (26*20) + (30*36) = 520 + 1080 = 1600.
At $30 per pound, selling price for the 56 pounds of mixture = 30*56 = 1680.
Profit = (selling price) - (cost price) = 1680 - 1600 = 80.
Profit percentage = (profit/cost) * 100 = (80/1600) * 100 = 5%.

The correct answer is B.
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by [email protected] » Sun Jun 04, 2017 10:24 am
Hi vaibhav101,

In this question, the total cost and total revenue are fairly straight-forward calculations, so let's start there:

Cost = (26)($20) + (30)($36) = $520 + $1080 = $1600 to purchase the rice
Revenue = (26+30)($30) = (56)($30) = $1680 in revenue from the sale of the rice

Thus, total profit = $1680 - $1600 = $80

We're asked for the profit as a percentage of the total cost. While you can certainly use the percentage change formula here, you might also notice a pattern that can save you a little time...

10% of $1600 = $160

Notice that profit was $80 though - that's exactly HALF of $160. Half of 10% is 5%. Thus...

$80 = 5% of 1600

Final Answer: B

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by Matt@VeritasPrep » Mon Jun 05, 2017 11:23 pm
Every kg he sells is 26/(26 + 30) parts $20 and 30/(26 + 30) parts $36. The cost of each kg to the trader is thus 26/56 * $20 + 30/56 * $36, or $28 + (4/7).

When he sells the mix for $30 per kg, he gets $30 / ($28 + 4/7) more than he paid, or 1.05 times what he paid, or 5% more.
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by Matt@VeritasPrep » Mon Jun 05, 2017 11:28 pm
If that last fraction is tough to manipulate without a calculator, here's the trick:

30 / (28 + 4/7) =>

30 / ((28*7 + 4)/7) =>

210/(28*7 + 4) =>

105/(14*7 + 2) =>

105/100
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Re: Problem solving : profit and loss

by Scott@TargetTestPrep » Sun Feb 16, 2020 7:54 am
vaibhav101 wrote: ↑
Sun Jun 04, 2017 2:46 am
 A trader mixes 26kg of rice at $20 per kg with 30kg of other variety at $36 per kg and sells the mixture at $30per kg. His profit % is
A zero
B 5
C 8
D 10
E -4
The cost is 26 x 20 + 30 x 36 = 520 + 1080 = $1600.

The revenue is 30 x (26 + 30) = 30 x 56 = $1680.

Therefore, the profit is 1680 - 1600 = $80, and the profit is:

80/1600 = 1/20 = 0.05 = 5% of the cost.

Answer: B

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