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Bunuel
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10 litres are removed from 80 litres of solution of milk and water hav 11 Jan 2020, 06:59
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65% (hard)

Question Stats:

65% (02:36) correct 35% (02:46) wrong based on 225 sessions

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10 litres are removed from 80 litres of solution of milk and water having ratio of milk and water as 4 : 3 and replaced with water. This operation is done a total of three times. What is the quantity of milk in the solution?

A. 245/8 litres
B. 247/8 litres
C. 249/8 litres
D. 250/8 litres
E. 255/8 litres
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10 litres are removed from 80 litres of solution of milk and water hav 12 Jan 2020, 07:59
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Bunuel
10 litres are removed from 80 litres of solution of milk and water having ratio of milk and water as 4 : 3 and replaced with water. This operation is done a total of three times. What is the quantity of milk in the solution?

A. 245/8 litres
B. 247/8 litres
C. 249/8 litres
D. 250/8 litres
E. 255/8 litres
Show more

Initial quantity of milk= 80*(4/7)=320/7
Quantity after three successive removal=\((320/7)*(1-10/80)^3\)
=245/8
A:)
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10 litres are removed from 80 litres of solution of milk and water hav 11 Jan 2020, 07:00
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Bunuel
10 litres are removed from 80 litres of solution of milk and water having ratio of milk and water as 4 : 3 and replaced with water. This operation is done a total of three times. What is the quantity of milk in the solution?

A. 245/8 litres
B. 247/8 litres
C. 249/8 litres
D. 250/8 litres
E. 255/8 litres
Show more

TWIN QUESTION: https://gmatclub.com/forum/10-litres-ar ... 14164.html
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10 litres are removed from 80 litres of solution of milk and water hav 07 Jun 2021, 23:23
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satya2029
Bunuel
10 litres are removed from 80 litres of solution of milk and water having ratio of milk and water as 4 : 3 and replaced with water. This operation is done a total of three times. What is the quantity of milk in the solution?

A. 245/8 litres
B. 247/8 litres
C. 249/8 litres
D. 250/8 litres
E. 255/8 litres

Initial quantity of milk= 80*(4/7)=320/7
Quantity after three successive removal=\((320/7)*(1-10/80)^3\)
=245/8
A:)
Show more

satya2029
How does this formula work?

If the 10 litres is removed and replaced with milk then?

Quantity after three successive removal=\((320/7)*(1+10/80)^3\) ??
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10 litres are removed from 80 litres of solution of milk and water hav 08 Mar 2022, 22:52
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Total quantity of mixture = 80 L
Ratio of Milk & Water => \(\frac{M}{W}\) = \(\frac{4}{3}\)
4x+3x = 80
7x = 80
x = \(\frac{80}{7}\)

Quantity of Milk = 4x = \(\frac{320}{7}\)

Quantity of Water = 3x = \(\frac{240}{7}\)

10 Liters of mixture is replaced with water and 10 liters of mixture would contain:

Milk = \(\frac{4}{7}*10\) = \(\frac{40}{7}\)

Water = \(\frac{3}{7}*10\) = \(\frac{30}{7}\)

Milk and water remaining after replacement:

Milk = \(\frac{320}{7}-\frac{40}{7}\) = \(\frac{280}{7}\) = 40 L

Water = \(\frac{240}{7}-\frac{30}{7}+10\) = \(\frac{280}{7}\) = 40 L

New ratio of Milk and Water => \(\frac{M}{W}\) = \(\frac{1}{1}\)

Again, 10 Liters of mixture is replaced with water and 10 liters of mixture would contain:

Milk = \(\frac{1}{2}*10\) = \(5\)

Water = \(\frac{1}{2}*10\) = \(5\)

Milk and water remaining after replacement:

Milk = \(40-5\) = 35 L

Water = \(40-5+10\) = 45 L

New ratio of Milk and Water => \(\frac{M}{W}\) = \(\frac{7}{9}\)

And again, 10 Liters of mixture is replaced with water and 10 liters of mixture would contain:

Milk = \(\frac{7}{16}*10\) = \(\frac{35}{8}\)

Milk remaining after replacement:

Milk = \(35-\frac{35}{8}\) = \(\frac{245}{8}\) (A)

Bunuel chetan2u is there a quicker way to solve this question?
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10 litres are removed from 80 litres of solution of milk and water hav 11 Jul 2022, 03:26
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satya2029
Bunuel
10 litres are removed from 80 litres of solution of milk and water having ratio of milk and water as 4 : 3 and replaced with water. This operation is done a total of three times. What is the quantity of milk in the solution?

A. 245/8 litres
B. 247/8 litres
C. 249/8 litres
D. 250/8 litres
E. 255/8 litres

Initial quantity of milk= 80*(4/7)=320/7
Quantity after three successive removal=\((320/7)*(1-10/80)^3\)
=245/8
A:)
Show more

Thank you for this simple solution :)
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10 litres are removed from 80 litres of solution of milk and water hav 08 May 2024, 09:43
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I have tried to solve this question using this formulae. Kindly check . KarishmaB

Since  after taking out 10 litres of solution , water is added , we will use the formulae from the milk's persepctive.

FInal amount of the milk = Initial amount  of the milk ( amount left after taking out 10 litres / total amount of the solution ) ^ 3

= 80* 4/ 7 * (( 80 - 10) / 80)^ 3

= 320 / 7 * (7/8)^3
=320/7 * 343 /512
= 49*5 / 8
= 245/8
KarishmaB Kindly check.­
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10 litres are removed from 80 litres of solution of milk and water hav 25 May 2025, 20:47
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