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# A milk-man mixes water equal to 20% of the quantity of milk he has, to

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Joined: 08 Nov 2019
Posts: 2
A milk-man mixes water equal to 20% of the quantity of milk he has, to  [#permalink]

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Updated on: 26 Dec 2019, 00:08
3
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Difficulty:

45% (medium)

Question Stats:

68% (02:31) correct 32% (02:39) wrong based on 28 sessions

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A milk-man mixes water equal to 20% of the quantity of milk he has, to the milk. Suspecting that his customers will notice the dilution, he decides to add pure milk to the mixture such that the ratio of milk and water increases to 17 : 3. If he had added 12 litres of water, how much litres of milk will he need to add.

A. 6
B. 8
C. 10
D. 12
E. 15

Originally posted by Abhattarai03 on 25 Dec 2019, 21:37.
Last edited by Bunuel on 26 Dec 2019, 00:08, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: A milk-man mixes water equal to 20% of the quantity of milk he has, to  [#permalink]

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25 Dec 2019, 21:52
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Hi Abhattarai03, welcome to GC!

My Approach:

Given: Water Added(12L) = 20% of Initial Milk Quantity
We get Milk Quantity = 60L

As more Milk(say x litres) was added to mixture making final ratio(M:W) as 17:3

equate the ratios-> x+60:12 = 17:3

We get x = 8, IMO Option B

One Small Request, I understand it is your first post on GC, please arrange the options in vertical order similar to other posts on GC. Thank you!
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Re: A milk-man mixes water equal to 20% of the quantity of milk he has, to  [#permalink]

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26 Dec 2019, 05:26
so the result is a solution with $$\frac{100}{120}$$ milk solution = $$\frac{5}{6}$$

by using the alligation method, we can find that the ratio of the adulterated to the pure is 9:1

if the water was 12, then the milk in the adulterated was 60, and the adulterated milk was 72 liters,
so the pure milk was 8 liters.
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A milk-man mixes water equal to 20% of the quantity of milk he has, to  [#permalink]

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26 Dec 2019, 20:30
He adds water in the milk at 20% ratio
thus 12 = 20% of M
or M = 60
to add more milk ratio should be $$17:3$$
thus
let extra milk added be x
so
$$\frac{60+x}{12 }= \frac{17}{3}$$
or x = 8
B
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A milk-man mixes water equal to 20% of the quantity of milk he has, to   [#permalink] 26 Dec 2019, 20:30