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A dishonest person wants to make a profit on the selling of

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guerrero25
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A dishonest person wants to make a profit on the selling of [#permalink] New post   02 Oct 2013, 17:32
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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
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Re: A dishonest person wants to make a profit on the selling of [#permalink] New post   02 Oct 2013, 20:47
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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

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 :-)
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Re: A dishonest person wants to make a profit on the selling of [#permalink] New post   27 Jan 2015, 22:28
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To achieve profit of 20% on "Pure Milk", its cost price should be \(= 36 * \frac{100}{120} = 30\)

However, given that cost price of "Pure Milk" = 33

1 litre "Pure Milk" is obtained in 33$, so "Pure Milk" obtained in 30$ \(= \frac{30}{33}\)

Water required to be added \(= 1 - \frac{30}{33}= \frac{3}{33}\)

Ratio of Water : Milk \(= \frac{\frac{3}{33}}{\frac{30}{33}} = \frac{3}{30} = \frac{1}{10}\)

Answer = B
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Re: A dishonest person wants to make a profit on the selling of [#permalink] New post   02 Oct 2013, 20:51
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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] New post   05 May 2016, 00:55
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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


Similar questions to practice:
a-dishonest-milkman-sells-a-40-liter-mixture-of-milk-and-water-that-co-192299.html
a-dishonest-milkman-wants-to-make-a-profit-on-the-selling-of-164753.html
a-dishonest-grocer-professes-to-sell-pure-butter-at-cpst-price-but-he-108766.html
merchant-makes-a-profit-of-20-on-selling-price-97059.html
a-merchant-claims-a-loss-of-4-on-coffee-but-uses-a-weight-o-167197.html
a-shop-owner-professes-to-sell-his-articles-at-certain-cost-127746.html
katrina-has-a-wheat-business-she-purchases-wheat-from-a-135499.html
a-man-cheats-while-buying-as-well-as-while-selling-while-135183.html
a-trader-cheats-both-his-supplier-and-customer-by-using-117512.html
a-dishonest-dealer-claims-to-sell-a-product-at-its-cost-pric-160822.html
a-shop-owner-professes-to-sell-his-articles-at-certain-cost-127746.html
if-a-trader-by-means-of-false-measures-gains-20-while-buy-122690.html

Hope this helps.
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Re: A dishonest person wants to make a profit on the selling of [#permalink] New post   26 May 2016, 10:33
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] New post   26 May 2016, 20:37
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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] New post   21 Aug 2016, 11:28
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] New post   15 Nov 2018, 19:26
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] New post   15 Apr 2021, 09:21
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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