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# A milkman mixes 20 litres of water with 80 litres of milk.

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Intern
Joined: 26 Sep 2018
Posts: 10
A milkman mixes 20 litres of water with 80 litres of milk.  [#permalink]

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01 Nov 2018, 06:44
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Difficulty:

25% (medium)

Question Stats:

80% (01:54) correct 20% (02:06) wrong based on 147 sessions

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A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk?

a. 2:3
b. 1:2
c. 1:3
d. 3:4
e. 1:1
NUS School Moderator
Joined: 18 Jul 2018
Posts: 1020
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: A milkman mixes 20 litres of water with 80 litres of milk.  [#permalink]

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01 Nov 2018, 07:03
3
Total quantity = 100 litres. the ratio of water to milk = 1:4
25% is sold.
remaining = 75 litres.
the quantity of water remaining = 75/5 = 15 litres.
quantity of milk remaining = 75*4/5 = 60 litres.
Now 25 liters of water is added.
so 40 liters of water and 60 liters of milk.
The ratio becomes $$2:3$$

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Manager
Joined: 10 Dec 2017
Posts: 85
Location: India
Re: A milkman mixes 20 litres of water with 80 litres of milk.  [#permalink]

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01 Nov 2018, 07:44
RhythmGMAT wrote:
A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk?

a. 2:3
b. 1:2
c. 1:3
d. 3:4
e. 1:1

Total Quantity =100 litres
Water =20 litres, Milk =80 litres
W/M=1/4
W/(W+M)= 1/5
He sold 1/4th of the mixture means 25 litres of the mixture.
here W+M = 25 Litres
W= 5 litres , M = 20 Litres
so the remaining quantity in the mixture
W= 15 litres and M= 60 Litres
As he adds 25 litres of water in the mixture
W= 15+25= 40 Litres
M= 60 Litres
W/M=40/60
W/M=2/3
A:)
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Joined: 21 Jun 2018
Posts: 71
A milkman mixes 20 litres of water with 80 litres of milk.  [#permalink]

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02 Nov 2018, 04:11
RhythmGMAT wrote:
A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk?

a. 2:3
b. 1:2
c. 1:3
d. 3:4
e. 1:1

Initial ratio = 2:8

After 1/4th is sold, quantity left is 75litres
Water in mixture = 2/10 * 75 = 15litres
Milk in mixture = 8/10 *75 = 60 litres

new ratio = [15 litres + 25 litres (qty sold) ] : 60 litres

After simplification , answer is 2:3

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Re: A milkman mixes 20 litres of water with 80 litres of milk.  [#permalink]

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07 Jul 2019, 07:41
1
Just solved this using a fantastic method by VeritasKarishma for a similar problem which takes this problem a step further by repeating the removal/replacement twice: https://gmatclub.com/forum/a-20-litre-m ... fl=similar

Recapping her method to make sure I have full understanding:

So we are given the initial amounts of water, 20 liters, and milk, 80 liters, which gives us our initial ratios, 1/5 and 4/5 respectively, and a total volume of 100 liters. We know that since 25% or 25 liters of the initial mixture are removed (total volume 75 liters) and replaced by 25 liters of just water (total volume 100 liters), that the amount of milk has remained the same from the initial mixture to the new one. As long as we can find one ratio, we can find the other, so by finding the new ratio of milk in the new mixture we will be able to determine the new ratio of water to milk.

The formula for new ratio is thus initial ratio * (Total Volume/New Volume)^ n (number of times this same replacement occurs)
--> 4/5 * (75/100)^1
--> New ratio of milk is 3/5
--> New ratio of water is thus 2/5
--> New ratio of water to milk is 2:3
Manager
Joined: 28 Jan 2019
Posts: 125
Location: Peru
A milkman mixes 20 litres of water with 80 litres of milk.  [#permalink]

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07 Jul 2019, 08:08
Pretty easy one:

first you have the original mixture:

water 20
milk 80

Then you sell 1/4 of the mixture so you have

water 15
milk 60

and finally, you have to complete and get 100 but only fill the mixture with water, so :

water 15 +25
milk 60

so, the proportion is 40/60 = 2/3, answer is (A)
VP
Joined: 07 Dec 2014
Posts: 1224
Re: A milkman mixes 20 litres of water with 80 litres of milk.  [#permalink]

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07 Jul 2019, 08:46
GMATRhythm wrote:
A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk?

a. 2:3
b. 1:2
c. 1:3
d. 3:4
e. 1:1

current water liters=.75(20)+.25(100)→40
current milk liters=.75(80)→60
40:60=2:3
A
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: A milkman mixes 20 litres of water with 80 litres of milk.  [#permalink]

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08 Jul 2019, 05:44
jmwon wrote:
Just solved this using a fantastic method by VeritasKarishma for a similar problem which takes this problem a step further by repeating the removal/replacement twice: https://gmatclub.com/forum/a-20-litre-m ... fl=similar

Recapping her method to make sure I have full understanding:

So we are given the initial amounts of water, 20 liters, and milk, 80 liters, which gives us our initial ratios, 1/5 and 4/5 respectively, and a total volume of 100 liters. We know that since 25% or 25 liters of the initial mixture are removed (total volume 75 liters) and replaced by 25 liters of just water (total volume 100 liters), that the amount of milk has remained the same from the initial mixture to the new one. As long as we can find one ratio, we can find the other, so by finding the new ratio of milk in the new mixture we will be able to determine the new ratio of water to milk.

The formula for new ratio is thus initial ratio * (Total Volume/New Volume)^ n (number of times this same replacement occurs)
--> 4/5 * (75/100)^1
--> New ratio of milk is 3/5
--> New ratio of water is thus 2/5
--> New ratio of water to milk is 2:3

You have used the method perfectly. But note the wording carefully so that you don't get confused:

"New concentration of milk" = 3/5
So we have 3 parts milk in total 5 parts solution (hence water must be 2 parts)

New ratio of water:milk = 2:3
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Re: A milkman mixes 20 litres of water with 80 litres of milk.   [#permalink] 08 Jul 2019, 05:44
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