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Posts: 7
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Difficulty:
15%
(low)
Question Stats:
82% (01:54) correct
18%
(02:17)
wrong
based on 713
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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
A. 2:3
B. 1:2
C. 1:3
D. 3:4
E. 1:1
Chethan92
Joined: 18 Jul 2018
Last visit: 21 Apr 2022
Posts: 899
Location: India
Concentration: Operations, General Management
Schools: IIMB EPGP'22 (M)
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE:Engineering (Energy)
Products:
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 \(2:3\)
A is the answer.
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 \(2:3\)
A is the answer.
General Discussion
RhythmGMAT
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:)
RhythmGMAT
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
______________________________________________________________________
Kudosity Killed the Kat, but i won't mind if you showed me some
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
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
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)
_________________
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)
_________________
Make your mercy overcome your wrath
GMATRhythm
current water liters=.75(20)+.25(100)→40
current milk liters=.75(80)→60
40:60=2:3
A
jmwon
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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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
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
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.
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.
AdarshSambare
Joined: 29 Jan 2022
Last visit: 07 Sep 2026
Posts: 314
Concentration: General Management, Sustainability
GPA: 2
WE:Engineering (Manufacturing)
Posts: 314
Let Total quantity = 100 litres, rather than variable x or anything
water - 20
and milk - 80
so the ratio of water to milk
= 20:80
= 1:4
25% is sold, so 25 liters is sold
Remaining = 75 litres.
The quantity of water remaining
= 75*(1/5) [1 part water in 5 part solution]
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.
40:60
The ratio becomes A
2:3
Answer :
water - 20
and milk - 80
so the ratio of water to milk
= 20:80
= 1:4
25% is sold, so 25 liters is sold
Remaining = 75 litres.
The quantity of water remaining
= 75*(1/5) [1 part water in 5 part solution]
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.
40:60
The ratio becomes A
2:3
Answer :
Posts: 51
Water = 20L and Milk = 80L Total L = 100
Let's use Milk:
Final = Initial x (1-r)^k
Final = 80 x (1-(1/4))^1
Final = 60
This means that water will be 40. 40/60 = 2/3
Let's use Milk:
Final = Initial x (1-r)^k
Final = 80 x (1-(1/4))^1
Final = 60
This means that water will be 40. 40/60 = 2/3
GMATRhythm
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