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# A merchant has 1000 kg of sugar part of which he sells at 8% profit an

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Re: A merchant has 1000 kg of sugar part of which he sells at 8% profit an [#permalink]
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IMO C

Let the quantity sold at 18% profit = x
Quantity sold at 8% profit= 1000 -x
Overall Profit = 14%

=> 1.18x + 1.08(1000-x) = 1.14 * 10000
Solving for x, x= 600
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Re: A merchant has 1000 kg of sugar part of which he sells at 8% profit an [#permalink]
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Bunuel wrote:
A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is

A. 300
B. 400
C. 600
D. 500
E. 700

say 8% profit- small part, 18% profit big part
8.....14......18
B/S=3/2
B/B+S=3/5
B/1000=3/5
B=600
C:)
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Re: A merchant has 1000 kg of sugar part of which he sells at 8% profit an [#permalink]
Typical mixture problem.

Difference in percentage profit of both parts:
10%

Mid point: 13% can be achieved by 500 kg each.

Therefore, we need the closest option just above 100.

Only option is 600. (C)

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Re: A merchant has 1000 kg of sugar part of which he sells at 8% profit an [#permalink]
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8 is -6 than verage
14 average
18 is + 4 of average
So the 1000 will be divided at a rate of 4 to 6 or 400 to 600.
Since 18 is closer to the average the bigger part =600 will be attributed to it

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Re: A merchant has 1000 kg of sugar part of which he sells at 8% profit an [#permalink]
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A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is

A. 300
B. 400
C. 600
D. 500
E. 700

Solution:
Let, Cost price per kg sugar = Tk.1
Therefore, Cost of 1000 kg of sugar = Tk. 1000
Suppose, quantity sold at 18% profit = x kg and quantity sold at 8% profit = (1000 – x) kg

Now,
18x/100 + 8*(1000 – x)/100 = 18*1000/100
Or, 10x + 8000 = 18000
Or, 10x = 6000
Or, x = 600
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A merchant has 1000 kg of sugar part of which he sells at 8% profit an [#permalink]
Bunuel wrote:
A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is

A. 300
B. 400
C. 600
D. 500
E. 700

Solve using Weighted average:

A = Part which he sells at 8% profit
Qty. of A W1
B = Part which he sells at 18% profit
Qty. of B W2

The 2 quantities are sold at 14% profit.
So Avg = 14%

$$\frac{W1}{W2 } = \frac{(B-Avg)}{(Avg-A)}$$

$$= \frac{(18-14)}{(14-8)}$$

$$\frac{W1}{W2 }= \frac{2}{3}$$

$$W2 = \frac{3}{5} * 1000$$

W2 = 600
Option C
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Re: A merchant has 1000 kg of sugar part of which he sells at 8% profit an [#permalink]
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Bunuel wrote:
A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is

A. 300
B. 400
C. 600
D. 500
E. 700

Posted from my mobile device
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Re: A merchant has 1000 kg of sugar part of which he sells at 8% profit an [#permalink]
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Re: A merchant has 1000 kg of sugar part of which he sells at 8% profit an [#permalink]
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