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A merchant buys 200 kg of rice at $1.25 per kg, 400kg of wheat at $0.7 [#permalink]
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Bunuel wrote:
A merchant buys 200 kg of rice at $1.25 per kg, 400kg of wheat at $0.75 per kg and 300 kg of tea $0.5 per kg. He sells 100 kg rice at a loss of 25%, 100 kg wheat at a profit of 25% and 100 kg tea a profit of 30%. He then mixes the rest and sells 1/3rd of the mixture at $1 per kg. Approximately at what rate he should sell the remaining mixture, so that he earn a profit of 25% on the whole outlay?

(A) $1.00
(B) $1.06
(C) $1.08
(D) $1.12
(E) $1.15


A merchant buys 200 kg of rice at $1.25 per kg, 400kg of wheat at $0.75 per kg and 300 kg of tea $0.5 per kg.
He earns a profit of 25% on the whole outlay.

Total outlay \(= (200*1.25) + (400*0.75) + (300*0.5) = 250+300+150 = 700\)
Required profit \(= \frac{25}{100}*700 = 175\)

Stage 1: He sells 100 kg rice at a loss of 25%, 100 kg wheat at a profit of 25% and 100 kg tea a profit of 30%.
Profit \(= (-0.25*100*1.25) + (0.25*100*0.75) + (0.3*100*0.5) = -31.25 + 18.75 + 15 = 2.5\)

Stage 2: He then mixes the rest and sells 1/3rd of the mixture at $1 per kg.
Remaining mixture = 100 kilograms of rice + 300 kilograms of wheat + 200 kilograms of tea = 600 kilograms.
Cost per kilogram of the remaining 600-kilogram mixture \(=\frac{(100*1.25) + (300*0.75) + (200*0.50)}{600} = \frac{125+225+100}{600} = 0.75\)
Since 200 kilograms are sold at a price of $1 per kilogram -- implying a profit of 0.25 per kilogram -- the profit yielded \(= 200*0.25 = 50\)

Stage 3: Approximately at what rate he should sell the remaining mixture?
Amount of profit to be yielded in Stage 3 = (total required profit) - (Stage 1 profit) - (Stage 2 profit) \(= 175 - 2.5 - 50 = 122.5\)
Since 400 kilograms must yield $122.5 in profit, the required profit per kilogram \(= \frac{122.5}{400} =\) a bit more than 0.3
Since the cost of the remaining mixture = 0.75 per kilogram, we get:
Selling price per kilogram = (cost per kilogram) + (required profit per kilogram) = 0.75 + (a bit more than 0.3) = a bit more than 1.05

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Re: A merchant buys 200 kg of rice at $1.25 per kg, 400kg of wheat at $0.7 [#permalink]
Is this question worth practising ? Can a question so calculation intensive come in the real gmat ? MartyMurray KarishmaB
GMAT Club Bot
Re: A merchant buys 200 kg of rice at $1.25 per kg, 400kg of wheat at $0.7 [#permalink]
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