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How many pounds of salt at 50 cents/lb must be mixed

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Senior Manager
Joined: 15 Jun 2010
Posts: 361
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
How many pounds of salt at 50 cents/lb must be mixed [#permalink]

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07 Aug 2012, 13:26
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71% (02:55) correct 29% (02:44) wrong based on 245 sessions

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How many pounds of salt at 50 cents/lb must be mixed with 40 lbs of salt that costs 35 cents/lb so that a merchant will get 20% profit by selling the mixture at 48 cents/lb?

A) 20
B) 15
C) 40
D) 50
E) 25

Source: 4gmat
[Reveal] Spoiler: OA

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Joined: 19 Apr 2012
Posts: 27
Re: How many pounds of salt at 50 cents/lb must be mixed [#permalink]

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07 Aug 2012, 14:23
I would do it this way:

1,2(50x + 40*35 / x+40) = 48

Solve for x = 20, so it's A. The path is quite long, maybe somehone has some shortcuts.
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Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India
Re: How many pounds of salt at 50 cents/lb must be mixed [#permalink]

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07 Aug 2012, 21:59
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SOURH7WK wrote:
How many pounds of salt at 50 cents/lb must be mixed with 40 lbs of salt that costs 35 cents/lb so that a merchant will get 20% profit by selling the mixture at 48 cents/lb?

A) 20
B) 15
C) 40
D) 50
E) 25

Source: 4gmat

Selling price is 48 cents/lb
For a 20% profit, cost price should be 40 cents/lb (CP*6/5 = 48)

Basically, you need to mix 35 cents/lb (Salt 1) with 50 cents/lb (Salt 2) to get a mixture costing 40 cents/lb (Salt Avg)

weight of Salt1/weight of Salt2 = (Salt2 - SaltAvg)/(SaltAvg - Salt1) = (50 - 40)/(40 - 35) = 2/1
We know that weight of salt 1 is 40 lbs. Weight of salt 2 must be 20 lbs.

Check these posts for details of this method:
http://www.veritasprep.com/blog/2011/03 ... -averages/
http://www.veritasprep.com/blog/2011/04 ... -mixtures/
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Veritas Prep | GMAT Instructor
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 27 Jul 2012 Posts: 25 Re: How many pounds of salt at 50 cents/lb must be mixed [#permalink] Show Tags 08 Aug 2012, 04:26 First From: x*1.2=48 Thus for 20% profit the cost should be 40c/lb. Now fastest way is to use alligation. salt A Salt B 35 50 40 10 5 expalanation: 40-35=5 and 50-40=10 10:5 is the ratio in which A and B are mixed ie 2:1 if A is 40lbs then B is 20lbs Alligation is the fastest way for these kind of questions Intern Joined: 05 Aug 2012 Posts: 16 Location: United States (CO) Concentration: Finance, Economics GMAT Date: 01-15-2014 GPA: 2.62 WE: Research (Investment Banking) Re: How many pounds of salt at 50 cents/lb must be mixed [#permalink] Show Tags 08 Aug 2012, 14:14 I agree to find the price where 20% profit = 48 cents a bag, which is 1.2x=.48, so the cost you are looking for is .4 or 40 cents. Now just set average cost of materials = .4 Where x = pounds at price of 50 cents... (.5x + .35(40))/(x+40) = .4 gets you down to .1x=2 x = 20 , choice A Senior Manager Joined: 23 Oct 2010 Posts: 383 Location: Azerbaijan Concentration: Finance Schools: HEC '15 (A) GMAT 1: 690 Q47 V38 Re: How many pounds of salt at 50 cents/lb must be mixed [#permalink] Show Tags 08 Aug 2012, 22:41 1.2y=48 y=40 50x+35*40=40(x+40) x=20 _________________ Happy are those who dream dreams and are ready to pay the price to make them come true I am still on all gmat forums. msg me if you want to ask me smth Director Joined: 03 Aug 2012 Posts: 893 Concentration: General Management, General Management GMAT 1: 630 Q47 V29 GMAT 2: 680 Q50 V32 GPA: 3.7 WE: Information Technology (Investment Banking) Re: How many pounds of salt at 50 cents/lb must be mixed [#permalink] Show Tags 19 Apr 2014, 00:13 Alligation Says 50----------------------------------35 ---------------40------------------- 5------------------------------------10 Why 40 is because 1.2*40 = 48 at which it was sold. 50C:35C should be used in ratio 1:2 WKT, 35c used is 40 lbs then 50C used is 20 _________________ Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 15920 Re: How many pounds of salt at 50 cents/lb must be mixed [#permalink] Show Tags 04 Aug 2015, 20:27 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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 15920 Re: How many pounds of salt at 50 cents/lb must be mixed [#permalink] Show Tags 02 Sep 2016, 08:08 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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Director Joined: 07 Dec 2014 Posts: 706 How many pounds of salt at 50 cents/lb must be mixed [#permalink] Show Tags 02 Sep 2016, 13:43 (50x+1400)/5=(48x+1920)/6 10x+280=8x+320 x=20 SVP Joined: 05 Jul 2006 Posts: 1747 How many pounds of salt at 50 cents/lb must be mixed [#permalink] Show Tags 13 Nov 2016, 02:55 VeritasPrepKarishma wrote: SOURH7WK wrote: How many pounds of salt at 50 cents/lb must be mixed with 40 lbs of salt that costs 35 cents/lb so that a merchant will get 20% profit by selling the mixture at 48 cents/lb? A) 20 B) 15 C) 40 D) 50 E) 25 Source: 4gmat Selling price is 48 cents/lb For a 20% profit, cost price should be 40 cents/lb (CP*6/5 = 48) Basically, you need to mix 35 cents/lb (Salt 1) with 50 cents/lb (Salt 2) to get a mixture costing 40 cents/lb (Salt Avg) weight of Salt1/weight of Salt2 = (Salt2 - SaltAvg)/(SaltAvg - Salt1) = (50 - 40)/(40 - 35) = 2/1 We know that weight of salt 1 is 40 lbs. Weight of salt 2 must be 20 lbs. Answer (A) Check these posts for details of this method: http://www.veritasprep.com/blog/2011/03 ... -averages/ http://www.veritasprep.com/blog/2011/04 ... -mixtures/ Hi Karishma, I am trying to work with profits using the number line and it aint working , could you please give me your insight on what is going wrong with my method. loss if selling 100% of the 50 cents salt (salt A) is 2/50 and profit of selling 100% 35% salt (Salt B)is 13/35 , the target profit is a weighted mix of both profits (1/5) Loss from ( 100% Salt A)-14/350........(7 parts) ..................70/350..............(5 parts)..........130/350 (profit from 100% Salt B) Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7440 Location: Pune, India Re: How many pounds of salt at 50 cents/lb must be mixed [#permalink] Show Tags 14 Nov 2016, 05:13 yezz wrote: VeritasPrepKarishma wrote: SOURH7WK wrote: How many pounds of salt at 50 cents/lb must be mixed with 40 lbs of salt that costs 35 cents/lb so that a merchant will get 20% profit by selling the mixture at 48 cents/lb? A) 20 B) 15 C) 40 D) 50 E) 25 Source: 4gmat Selling price is 48 cents/lb For a 20% profit, cost price should be 40 cents/lb (CP*6/5 = 48) Basically, you need to mix 35 cents/lb (Salt 1) with 50 cents/lb (Salt 2) to get a mixture costing 40 cents/lb (Salt Avg) weight of Salt1/weight of Salt2 = (Salt2 - SaltAvg)/(SaltAvg - Salt1) = (50 - 40)/(40 - 35) = 2/1 We know that weight of salt 1 is 40 lbs. Weight of salt 2 must be 20 lbs. Answer (A) Check these posts for details of this method: http://www.veritasprep.com/blog/2011/03 ... -averages/ http://www.veritasprep.com/blog/2011/04 ... -mixtures/ Hi Karishma, I am trying to work with profits using the number line and it aint working , could you please give me your insight on what is going wrong with my method. loss if selling 100% of the 50 cents salt (salt A) is 2/50 and profit of selling 100% 35% salt (Salt B)is 13/35 , the target profit is a weighted mix of both profits (1/5) Loss from ( 100% Salt A)-14/350........(7 parts) ..................70/350..............(5 parts)..........130/350 (profit from 100% Salt B) If you work with profit, the cost price is the weight. Check here: https://www.veritasprep.com/blog/2014/1 ... -averages/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Posts: 1747
Re: How many pounds of salt at 50 cents/lb must be mixed [#permalink]

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17 Nov 2016, 13:20
yezz wrote:
VeritasPrepKarishma wrote:
SOURH7WK wrote:
How many pounds of salt at 50 cents/lb must be mixed with 40 lbs of salt that costs 35 cents/lb so that a merchant will get 20% profit by selling the mixture at 48 cents/lb?

A) 20
B) 15
C) 40
D) 50
E) 25

Source: 4gmat

Selling price is 48 cents/lb
For a 20% profit, cost price should be 40 cents/lb (CP*6/5 = 48)

Basically, you need to mix 35 cents/lb (Salt 1) with 50 cents/lb (Salt 2) to get a mixture costing 40 cents/lb (Salt Avg)

weight of Salt1/weight of Salt2 = (Salt2 - SaltAvg)/(SaltAvg - Salt1) = (50 - 40)/(40 - 35) = 2/1
We know that weight of salt 1 is 40 lbs. Weight of salt 2 must be 20 lbs.

Check these posts for details of this method:
http://www.veritasprep.com/blog/2011/03 ... -averages/
http://www.veritasprep.com/blog/2011/04 ... -mixtures/

Hi Karishma,

I am trying to work with profits using the number line and it aint working , could you please give me your insight on what is going wrong with my method.

loss if selling 100% of the 50 cents salt (salt A) is 2/50 and profit of selling 100% 35% salt (Salt B)is 13/35 , the target profit is a weighted mix of both profits (1/5)

Loss from ( 100% Salt A)-14/350........(7 parts) ..................70/350..............(5 parts)..........130/350 (profit from 100% Salt B)

I get it now , to use weighted average in profit problems , we must use the multiplicative relation of selling price and cost , i,e

selling price/cost = 1.x where x is the profit and hence we use cost as weights ( if we use a weighted average formula) since in a multiplicative relation profit is selling price/unit of cost.

in our case here

selling price / cost = 1.2 , thus [48 *( 40+x)] / (50x+35*40) = 1.2 and x = 20
Re: How many pounds of salt at 50 cents/lb must be mixed   [#permalink] 17 Nov 2016, 13:20
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