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Re: A dishonest person wants to make a profit on the selling of [#permalink]
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mikemcgarry wrote:
guerrero25 wrote:
A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk?
(A) 1:20
(B) 1:10
(C) 1:8
(D) 1:4
(E) 1:2

Dear guerrero25,
I'm happy to help with this. :-)

First of all, let's consider 1 liter of the stuff he is going to sell --- naive customers think it's pure milk, but we know it's some milk-water mixture. He is going to sell this liter of milk-water for $36.

This $36 should be a 20% increase over cost. Here, we need to think about percentage increases as multipliers. See this blog for more info:
https://magoosh.com/gmat/2012/understand ... -the-gmat/
Using multipliers
(cost)*1.20 = $36
cost = 36/1.2 = 360/12 = $30

If he wants a 20% increase over cost on the sale of one liter of his milk-water, the cost has to be $30.

Well, a liter of milk costs $33, so if he is going to use just $30 of milk in his mixture, that's 30/33 = 10/11 of a liter. If milk is 10/11 of the liter, then water is 1/11 of the liter, and the ratio of water to milk is 1:10. Answer choice (B)

Does all this make sense?
Mike :-)



Great solution, as always Mike! Thank you :)
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Re: A dishonest person wants to make a profit on the selling of [#permalink]
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Re: A dishonest person wants to make a profit on the selling of [#permalink]
mikemcgarry wrote:
guerrero25 wrote:
A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk?
(A) 1:20
(B) 1:10
(C) 1:8
(D) 1:4
(E) 1:2

Dear guerrero25,
I'm happy to help with this. :-)

First of all, let's consider 1 liter of the stuff he is going to sell --- naive customers think it's pure milk, but we know it's some milk-water mixture. He is going to sell this liter of milk-water for $36.

This $36 should be a 20% increase over cost. Here, we need to think about percentage increases as multipliers. See this blog for more info:
https://magoosh.com/gmat/2012/understand ... -the-gmat/
Using multipliers
(cost)*1.20 = $36
cost = 36/1.2 = 360/12 = $30

If he wants a 20% increase over cost on the sale of one liter of his milk-water, the cost has to be $30.

Well, a liter of milk costs $33, so if he is going to use just $30 of milk in his mixture, that's 30/33 = 10/11 of a liter. If milk is 10/11 of the liter, then water is 1/11 of the liter, and the ratio of water to milk is 1:10. Answer choice (B)

Does all this make sense?
Mike :-)


Approached this question as follows -

He needs to make a profit of 20%, which means he needs to sell the milk +water combination for 39.6 (20% of 33 +33)
Now, he plans to sell 1 liter of this solution of milk and water for 36. which means he needs to sell 1.1 liters of this solution to earn 39.6. (36 for 1 liter and so 39.6 for 1.1 liters)

Hence the water added would be .1 liter.

Therefore the ratio of water to milk is .1/1 = 1/10

Please suggest if this approach is correct. Thanks
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Re: A dishonest person wants to make a profit on the selling of [#permalink]
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guerrero25 wrote:
A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk?
(A)1:20
(B) 1:10
(C) 1:8
(D)1:4
(E)1:2


You can also use weighted averages.

Selling cost is $36 with profit of 20%.

Cost Price * 6/5 = $36
Cost Price = $30

Ww/Wm = (33 - 30)/(30 - 0) = 1/10 (Using weighted average formula discussed here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/03 ... -averages/)

Put 1 part water for every 10 parts of milk. Answer (B)
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Re: A dishonest person wants to make a profit on the selling of [#permalink]
11 x 36 = 10 x 33 x 1.2

so...

1:10
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Re: A dishonest person wants to make a profit on the selling of [#permalink]
Why does the answer assume there's 1 liter of the liquid mixture?
If you sell the liquid as "milk" for $36, that volume must be $36/$33 liters because the price of milk is $33 per liter.
Paying $30 (for the $6 profit), you get $30/$33 liters of milk. The volume of the liquid must be 36/33 liters to sell for $36. Add 6/33 liters of water to make up the remaining volume. The ratio of water : milk is 6:30 or 1:5

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Re: A dishonest person wants to make a profit on the selling of [#permalink]
mikemcgarry wrote:
guerrero25 wrote:
A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk?
(A) 1:20
(B) 1:10
(C) 1:8
(D) 1:4
(E) 1:2

Dear guerrero25,
I'm happy to help with this. :-)

First of all, let's consider 1 liter of the stuff he is going to sell --- naive customers think it's pure milk, but we know it's some milk-water mixture. He is going to sell this liter of milk-water for $36.

This $36 should be a 20% increase over cost. Here, we need to think about percentage increases as multipliers. See this blog for more info:
https://magoosh.com/gmat/2012/understand ... -the-gmat/
Using multipliers
(cost)*1.20 = $36
cost = 36/1.2 = 360/12 = $30

If he wants a 20% increase over cost on the sale of one liter of his milk-water, the cost has to be $30.

Well, a liter of milk costs $33, so if he is going to use just $30 of milk in his mixture, that's 30/33 = 10/11 of a liter. If milk is 10/11 of the liter, then water is 1/11 of the liter, and the ratio of water to milk is 1:10. Answer choice (B)

Does all this make sense?
Mike :-)


Assume M milk quantity and W water quantity in liters

Let's assume x= 33*(M/(M+W))+0*(W/M+W))= 33 (M/(M+W)) X EQUALS the weighted average of the prices with weights on the quantities

We know that the seller must make 20% of profit over cost by selling the mixture at 36$.
Thus (36-X)/X=0,20
(36-x)/X=20/100
X=30

Thus X=30= 33(M/(M+V)) and we get M/ M+W = 10/11

Thus for each 10/11 of milk we have 1/11 of water, thus their ratio must be 1:10.
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