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sugar mixtures

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by abhishekswamy » Sun Jul 24, 2011 9:07 am
A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 17% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?
Possible Answers
Selected Possible Answer


A. 70 lbs


B. 40 lbs


C. 30 lbs


D. 50 lbs


E. 60 lbs
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by knight247 » Sun Jul 24, 2011 9:41 am
Answer is A

Let the amount of sugar sold at 7% profit be x and amount sold at 17% profit be y
Given that x+y=100..........(1)

for the x lbs
Let cost price be $C per lb
Total cost is xC

Sale Price=xC+7(xC)/100
= 1.07xC..........(2)

for the y lbs
cost price/lb is the same as cost price for previous amount which is $C/lb
Total cost is yC

Sale Price=yC+17(yC)100
=yc+0.17yC= 1.17yC.........(3)

Total sale price from 2 and 3
1.07xC+1.17yC......(4)

Total cost price is xC+yC

As per given information, he made a 10% profit on the sale of the entire 100 lbs of sugar

Sale Price-Cost price=10(Cost Price)/100
1.07xC+1.17yC-xC-yC=(0.1)(xC+yC)
0.07xC+0.17yC=0.1xC+0.1yC

0.07x+0.17y=0.1x+0.1y
Multiplying by 100
7x+17y=10x+10y
7y=3x
y=3x/7

Substituting this value in x+y=100
x+3x/7=100
7x+3x=700
10x=700
x=70

Hence A
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by GMATGuruNY » Sun Jul 24, 2011 9:45 am
abhishekswamy wrote:A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 17% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?
Possible Answers
Selected Possible Answer


A. 70 lbs


B. 40 lbs


C. 30 lbs


D. 50 lbs


E. 60 lbs
This is a weighted average/mixture problem.
We need to combine the sugar sold at a 7% profit with the sugar sold at a 17% profit so that the mixture yields a 10% profit.
Using alligation:

The proportion of each element in the mixture is the distance between the percentage attributed to the other element in the mixture and the percentage attributed to the final mixture.

Proportion sold at a 7% profit = 17-10 = 7.
Proportion sold at a 17% profit = 10-7 = 3.
Portion at a 7% profit: Portion at a 17% profit = 7:3.

Since 7+3 = 10, 7/10 of the sugar is sold at a 7% profit.
7/10 * 100 = 70 pounds.

The correct answer is A.
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by abhishekswamy » Sun Jul 24, 2011 10:02 am
GMATGuruNY wrote:
abhishekswamy wrote:A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 17% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?
Possible Answers
Selected Possible Answer


A. 70 lbs


B. 40 lbs


C. 30 lbs


D. 50 lbs


E. 60 lbs
This is a weighted average/mixture problem.
We need to combine the sugar sold at a 7% profit with the sugar sold at a 17% profit so that the mixture yields a 10% profit.
Using alligation:

The proportion of each element in the mixture is the distance between the percentage attributed to the other element in the mixture and the percentage attributed to the final mixture.

Proportion sold at a 7% profit = 17-10 = 7.
Proportion sold at a 17% profit = 10-7 = 3.
Portion at a 7% profit: Portion at a 17% profit = 7:3.

Since 7+3 = 10, 7/10 of the sugar is sold at a 7% profit.
7/10 * 100 = 70 pounds.

The correct answer is A.
Hi Guru,

Can you please elaborate this portion:

The proportion of each element in the mixture is the distance between the percentage attributed to the other element in the mixture and the percentage attributed to the final mixture.

Proportion sold at a 7% profit = 17-10 = 7.
Proportion sold at a 17% profit = 10-7 = 3.
Portion at a 7% profit: Portion at a 17% profit = 7:3.

How you made the above calculations?What is the general rule?
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by GMATGuruNY » Sun Jul 24, 2011 10:41 am
abhishekswamy wrote:
GMATGuruNY wrote:
abhishekswamy wrote:A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 17% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?
Possible Answers
Selected Possible Answer


A. 70 lbs


B. 40 lbs


C. 30 lbs


D. 50 lbs


E. 60 lbs
This is a weighted average/mixture problem.
We need to combine the sugar sold at a 7% profit with the sugar sold at a 17% profit so that the mixture yields a 10% profit.
Using alligation:

The proportion of each element in the mixture is the distance between the percentage attributed to the other element in the mixture and the percentage attributed to the final mixture.

Proportion sold at a 7% profit = 17-10 = 7.
Proportion sold at a 17% profit = 10-7 = 3.
Portion at a 7% profit: Portion at a 17% profit = 7:3.

Since 7+3 = 10, 7/10 of the sugar is sold at a 7% profit.
7/10 * 100 = 70 pounds.

The correct answer is A.
Hi Guru,

Can you please elaborate this portion:

The proportion of each element in the mixture is the distance between the percentage attributed to the other element in the mixture and the percentage attributed to the final mixture.

Proportion sold at a 7% profit = 17-10 = 7.
Proportion sold at a 17% profit = 10-7 = 3.
Portion at a 7% profit: Portion at a 17% profit = 7:3.

How you made the above calculations?What is the general rule?
We need to determine how much weight must be given to each element in the mixture.
10% is closer to 7% than to 17%, so we know that more weight must be given to the portion sold at a 7% profit.
To determine the correct ratio, we examine the distances between the percentages. The process is called alligation:

7%----10%--------------17%

|---3--||--------7--------|

The distance between 7% and 10% tells us how much weight must be given to the sugar sold at a 17% profit:
Portion sold at 17% profit = 10-7 = 3.

The distance between 10% and 17% tells us how much weight must be given to the sugar sold at a 7% profit:
Portion sold at 7% profit = 17-10 = 7.

Thus, we get the following ratio:
Portion sold at a 17% profit : Portion sold at a 7% profit = 3:7.

The sum of the numbers in the ratio = 3+7 = 10.
Thus, out of every 10 pounds sold, 7 pounds must be sold at a 7% profit.
In other words, the amount sold at a 7% profit = 7/10 of the total weight.
Since the total weight is 100 pounds, the amount sold at a 7% profit = 7/10 * 100 = 70.
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