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A merchant has 100 lbs of sugar, part of which he sells at 7

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Director
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A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

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New post 26 Jul 2010, 08:50
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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?

A. 70 lbs
B. 40 lbs
C. 30 lbs
D. 50 lbs
E. 60 lbs

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Re: Mixture with profit problem [#permalink]

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New post 26 Jul 2010, 09:14
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rxs0005 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?



A. 70 lbs


B. 40 lbs


C. 30 lbs


D. 50 lbs


E. 60 lbs


Is it A? (70lbs)

7% --> 3% difference to 10%
17% --> 7% difference to 10%

so 7:3 is the required mixture (since we are closer to 7 than to 17), hence 70:30.

Cheers,

André
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Re: Mixture with profit problem [#permalink]

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New post 26 Jul 2010, 09:28
Solution by AndreG is correct IMO. I'd doubt that this is a 700 level question (seems to be a pretty straightforward mixture problem), rather a 600 level question (or even lower).

You can also solve this problem algebraically:

Variable we look for:
x = amount of sugar sold at 7% profit

Equation:
10%*100 lbs = x*7% + (100-x)*17%

Solving for x you get x = 70 lbs
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Re: Mixture with profit problem [#permalink]

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New post 26 Jul 2010, 09:43
70 is right

and also its not a 700 level problem i accidentally added that tag i guess

thanks !
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Re: Mixture with profit problem [#permalink]

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New post 02 Feb 2014, 10:50
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rxs0005 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?



A. 70 lbs


B. 40 lbs


C. 30 lbs


D. 50 lbs


E. 60 lbs


I use differentials for these types of weighted average problems

We have X at 7% and 100 - x at 17% give a weighted average of 10%

Hence -3x + 7(100-x) = 0

Solving x = 70

A
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Re: A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

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New post 18 Feb 2015, 09:21
1
I feel that putting the percentages into fractions makes the problem quicker to solve.

100(x)(7/100)+(100(1-x)) (17/100)=100(10/100)

7x+17-17x=10
-10x=-7
x=7/10

100lbs x (7/10) = 70lbs

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Re: A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

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New post 18 Feb 2015, 22:37
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Hi All,

These types of "weighted average" questions can be solved in a variety of ways, so you can choose whichever method you find easiest/fastest. Here's another variation on the Weighted Average Formula:

A = # of pounds sold at 7% profit
B = # of pounds sold at 17% profit
A+B = 100 pounds

(.07A + .17B)/(A+B) = .10

.07A + .17B = .1A + .1B
.07B = .03A
7B = 3A
7/3 = A/B

So, for every 7 pounds of A, we have 3 pounds of B.
With 100 pounds total, we have 70 pounds of A and 30 pounds of B.

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A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

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New post 24 Feb 2015, 02:22
jlgdr wrote:
rxs0005 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?



A. 70 lbs


B. 40 lbs


C. 30 lbs


D. 50 lbs


E. 60 lbs


I use differentials for these types of weighted average problems

We have X at 7% and 100 - x at 17% give a weighted average of 10%

Hence -3x + 7(100-x) = 0

Solving x = 70

A


Almost always I prefer using algebra for these problems, or else weighted averages (if I manage to notice the connection). However, I did like this solution a lot.

I am not sure I understand what it means to subtract 7% and 17% from 10% though. Could someone please explain the reasoning behing this?
Also, why is it -3x and +7(100-x) and not the opposite, if we are subtracting those from 10?

Thank you!
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Re: A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

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New post 24 Feb 2015, 20:13
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Hi pacifist85,

Differentials are essentially a sub-set of Calculus, which is a category of math that is NOT tested on the Official GMAT. While a Test Taker might be able to use this type of math to answer certain questions, it's not really worth focusing on (for much the same reason why you don't need to know Trigonometry to answer the Geometry questions that you'll see on Test Day. While that math might be use-able on certain questions, it's not tested).

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Re: A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

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New post 25 Feb 2015, 00:27
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Answer = A = 70

Using allegation method

7% ............................ 17%

................. 10% ................

(17-10) = 7 .................. (10-7) = 3

\(\frac{7}{7+3} * 100 = 70 Lbs\)
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Re: A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

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New post 20 Aug 2017, 06:17
Used the weighted avg formula learnt at a different question:
7 = x amount sold at 7% profit
100 - x = rest sold at 17% interest
10 = (17 - 7)
putting in formula
7 + (100 - x)10/100 (denominator here is 100 pounds) = 10 (overall profit)
x = 70 lbs
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Re: A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

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New post 20 Aug 2017, 06:18
Used the weighted avg formula learnt at a different question:
7 = x amount sold at 7% profit
100 - x = rest sold at 17% interest
10 = (17 - 7)
putting in formula
7 + (100 - x)10/100 (denominator here is 100 pounds) = 10 (overall profit)
x = 70 lbs
Re: A merchant has 100 lbs of sugar, part of which he sells at 7   [#permalink] 20 Aug 2017, 06:18
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A merchant has 100 lbs of sugar, part of which he sells at 7

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