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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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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?

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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

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.

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

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

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04 Aug 2015, 20:27

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

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02 Sep 2016, 08:08

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

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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.

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)

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.

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)

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.

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

gmatclubot

Re: How many pounds of salt at 50 cents/lb must be mixed
[#permalink]
17 Nov 2016, 13:20

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