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

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Re: A milkman mixes 20 litres of water with 80 litres of milk. [#permalink]
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]
1
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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
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Re: A milkman mixes 20 litres of water with 80 litres of milk. [#permalink]
1
Kudos
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)
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Re: A milkman mixes 20 litres of water with 80 litres of milk. [#permalink]
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
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Re: A milkman mixes 20 litres of water with 80 litres of milk. [#permalink]
2
Kudos
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]
In total the milkman has 20 + 80 = 100L of his solution.

1. 100L - 25L = 75L left.

2.75L x 4/5 = 60L milk left
75L x 1/5 = 15L milk left

3. He adds back 25L of water.
60 + (15 + 25) = 100L

4. The ratio of water to milk is now 40:60 = 2:3

A
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Re: A milkman mixes 20 litres of water with 80 litres of milk. [#permalink]
KarishmaB , kindly check my method and confirm whether I did it correctly.
The final concentration of milk = Initial concentration of milk * ( 1 - amount replaced / amount of the entire solution )
=80 * (1 - 25/100 ) = 80 * 3 /4 = 60 ltr.

Total amount is still same i.e 100 litres. Hence amount of water = 100 - 60 = 40 litres
Final ratio of water and milk = 40 : 60 = 2:3­
MartyMurray Kindly check.
Re: A milkman mixes 20 litres of water with 80 litres of milk. [#permalink]
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