Problem Solving

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

Hope this helps!

-Jay
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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

GMAT assassins aren't born, they're made,
Rich

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