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

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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 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.

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

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%

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

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18 Feb 2015, 04:18

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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

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

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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?

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).

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

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17 May 2016, 12:09

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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12 Aug 2017, 10:26

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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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

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

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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

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