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

Question

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

yashikaaggarwal · Answer

IMO C

Let the quantity sold at 8% profit = x
And the quantity sold at 18% profit = y.
=> 108*x/100+118*y/100 = (x+y)*114/100
=> 108x+118y=114x+114y
=> 4y = 6x => 2y = 3x
=> x/y = 2/3 
=> therefore, x:y = 2:3
=> dividing 1000 in 2:3 ratio we get y = 600 (1000*3/5)
The quantity sold at 18% profit= 600

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gurmukh · Answer

8x +18y =14(x+y)
4y=6x
x:y= 2:3
Quantity sold at 18% profit = 
 3/5×1000
 =600
Option C is the answer

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NitishJain · Answer

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

satya2029 · Answer

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:)

ritwikk2 · Answer

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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dimri10 · Answer

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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Jawad001 · Answer

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
Answer: 600

Shrey08 · Answer

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

Emdad · Answer

The answer is C.

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

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