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A merchant buys 200 kg of rice at $1.25 per kg, 400kg of wheat at $0.7 08 Mar 2021, 03:45
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95% (hard)

Question Stats:

58% (03:42) correct 42% (03:17) wrong based on 85 sessions

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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
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A merchant buys 200 kg of rice at $1.25 per kg, 400kg of wheat at $0.7 21 Mar 2021, 10:32
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Bunuel
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
Show more

Rice

Total C.P.= \(200*1.25= 250\)

\(100\) kg of rice C.P = \(100*1.25= 125\)

S.P of this \(100\) Kg ( At a loss of \(25\%\)) = \(.75*125= 93.75\)


Wheat

Total C.P. = \(400*.75= 300\)

\(100 \)Kg of wheat C.P \(=100*.75= 75\)

S.P of \(100\) Kg of wheat ( at a profit of \(25\%\))= \(1.25*75= 93.75\)

Tea

Total C.P. = \(300*.5= 150\)

\(100\) Kg of tea C.P\(= 50\)

S.P of \(100\) Kg ( at a profit of \(30\%\))\(= 1.3*50=65\)

So total quantity sold so far

\(100 +100 +100 = 300\)

Quantity remaining = \(900-300=600\)

\(\frac{1}{3}\) of \(600\) was sold at $1

So \(200\) was sold at $1

Remaining = \(400 \)kg's

Total revenue so far = \(93.75 +93.75+65+ 200= 452.5\)

Trader should make a profit of \(25\%\) on the whole outlay:

Total C.P= \(250+300+150=700\)

At a profit of \(25\% \)means = \(1.25 *700 =875 \)

So total revenue should be \(875\) for a profit of \(25\%\) on the whole outlay.

However so far we have only \(= 452.5 \)

Remaining amount = \(875-452.5= 422.5\)

Also remaining quantity that we have is \(400 \)

Hence remaining quantity should be sold \(\frac{422.5}{400} \approx 1.06 \) per kg for a profit of \(25\%\) on the whole outlay.

Ans-B

Hope it's clear.

(Huff...huff...)
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A merchant buys 200 kg of rice at $1.25 per kg, 400kg of wheat at $0.7 22 Mar 2021, 02:54
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I don't think the question overall is a tough question but it is extremely heavy on calculations and is difficult to get under 2 mins.
Is there any non calculative/ only logical way to go about thinking for this question?
Maybe to be able to at least take a calculated guess.
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A merchant buys 200 kg of rice at $1.25 per kg, 400kg of wheat at $0.7 22 Mar 2021, 13:07
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Bunuel
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
Show more

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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A merchant buys 200 kg of rice at $1.25 per kg, 400kg of wheat at $0.7 29 Jul 2025, 15:26
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