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# A milk vendor sells milk at Cost Price but still gains 20%. Find the

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Math Expert
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A milk vendor sells milk at Cost Price but still gains 20%. Find the  [#permalink]

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11 Nov 2019, 02:36
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48% (01:48) correct 52% (01:24) wrong based on 124 sessions

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A milk vendor sells milk at Cost Price but still gains 20%. Find the ratio of milk and water in every gallon that he sells.

A. 4:1
B. 5:1
C. 5:2
D. 6:1
E. None of these

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A milk vendor sells milk at Cost Price but still gains 20%. Find the  [#permalink]

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11 Nov 2019, 23:19
5
1
Say he buys 1 liter of pure milk at $10/liter. He has to sell this for$12 in order to make 20% profit on cost. By adding 0.2 liters of water, he can ensure that he does this while still selling at $10/liter (1.2L*$10=$12). So ratio of Milk to Water is 1:0.2 or 5:1. ANS: B ##### General Discussion Intern Joined: 12 Mar 2017 Posts: 9 Location: India Anup: Patel Concentration: Strategy, Economics GPA: 3 WE: Education (Education) Re: A milk vendor sells milk at Cost Price but still gains 20%. Find the [#permalink] ### Show Tags 11 Nov 2019, 05:35 Somehow getting Ans B (5:1)...but not so sure ! Intern Joined: 14 Feb 2017 Posts: 5 GMAT 1: 620 Q47 V28 A milk vendor sells milk at Cost Price but still gains 20%. Find the [#permalink] ### Show Tags 15 Nov 2019, 06:18 1 Cost price=selling price =1 so there's a change in quantity which allows the gain of 20 percent initial quantity 100 since same pricing water has been added becomes 120 20:100(w:M)1:5 hence option B Intern Status: Climbing the GMAT mountain Joined: 11 Feb 2018 Posts: 21 Location: Germany Concentration: Technology, Strategy Re: A milk vendor sells milk at Cost Price but still gains 20%. Find the [#permalink] ### Show Tags 20 Dec 2019, 06:59 1 Bunuel wrote: A milk vendor sells milk at Cost Price but still gains 20%. Find the ratio of milk and water in every gallon that he sells. A. 4:1 B. 5:1 C. 5:2 D. 6:1 E. None of these We can also solve this by using the profits-fundamentals: We just know he sells with a profit of 20%, So the Markup Percentage = 20% = $$\frac{1}{5}$$. And we want to find the actual cost price of the milk alone. Assume the Marked Price to be 1 unit. The formula for Markup Percentage is: $$\frac{MarkedPrice - Cost Price}{Cost Price} = \frac{1-x}{x} = \frac{1}{5}$$ Solve for x. -> $$x = \frac{5}{6}$$ Thus, the ratio is 5:1, Answer B. Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 9142 Location: United States (CA) Re: A milk vendor sells milk at Cost Price but still gains 20%. Find the [#permalink] ### Show Tags 22 Dec 2019, 20:47 Bunuel wrote: A milk vendor sells milk at Cost Price but still gains 20%. Find the ratio of milk and water in every gallon that he sells. A. 4:1 B. 5:1 C. 5:2 D. 6:1 E. None of these Are You Up For the Challenge: 700 Level Questions We can let the ratio of milk to water be 1 : n, and the cost price of 1 gallon of milk is$10. After mixing with water, we have 1 + n gallons of the milk mixture, and he sells every gallon of the mixture for $10. In the 1 + n gallons of the milk mixture, 1/(1 + n) of it is milk. We can create the equation where x is the number of gallons of milk in 1 gallon of the milk mixture: x/1 = 1/(1 + n) x = 1/(1 + n) So the selling price of milk by the vendor is 10/(1/(1 + n)) = 10(1 + n) per gallon (assuming water does not cost anything) and this is 120% of the cost price of$10 per gallon of milk. We can create the equation:

10(1 + n) = 1.2(10)

1 + n = 1.2

n = 0.2

So for every 1 gallon of milk, the vendor mixed it with 0.2 gallons of water. In other words, for every 5 gallons of milk, the vendor mixed it with 1 gallon of water.

Alternate Solution:

Suppose that the vendor bought 100 gallons of milk for c dollars. If the vendor made a profit of 20%, then it must be true that the vendor made a revenue of 1.2c dollars. Since the vendor sold the milk and water mixture at the same cost per gallon, it follows that the vendor sold 120 gallons of the mixture. Thus, the mixture contains 20 gallons of water for every 100 gallons of milk; which gives us a milk-to-water ratio of 5:1.

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Senior Manager
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A milk vendor sells milk at Cost Price but still gains 20%. Find the  [#permalink]

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25 Dec 2019, 20:49
M = Milk; C = COst price

1.2MC = (M+W)C

1.2M = M +W;

0.2M=W can also be written as 2/10M = W

therefore m/w = 10/2

Therefore 5:1
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Re: A milk vendor sells milk at Cost Price but still gains 20%. Find the  [#permalink]

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25 Dec 2019, 21:14
To ensure that he makes 20% profit by selling same amount of milk at same selling price he would have to add 20% water to it.
Elaborating:
Say cost price of Milk is $100 per 100 ltr (CP=$1/ltr)
So he would have to sell Milk + Water (100+20) mixture at $120 per 120 ltrs for Selling price to be equal to Cost price of the milk. (SP = CP=$1/ ltr)

Thus Milk: Water = 100: 20 = 5:1

Note: The question must mention that water is for free. Apparently, at some place water costs more than milk
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Joined: 13 Feb 2018
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GMAT 1: 640 Q48 V28
A milk vendor sells milk at Cost Price but still gains 20%. Find the  [#permalink]

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17 Jan 2020, 05:46
I solved this with picking numbers as well

Imagine:
Buys 100 liters of milk for $1 per liters, pays$100
He earns 20% gain while selling 1-liter concentrate for 1$, so his revenue is$120
We can deduce that he has sold 20 liters of water for \$1 per liter

Milk=100 liters
Water=20 Liters

Ratio milk to water= 5/1

IMO
Ans: B
A milk vendor sells milk at Cost Price but still gains 20%. Find the   [#permalink] 17 Jan 2020, 05:46
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