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# A 30-litre bucket contains a mixture of milk and water in the ratio 2:

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Intern
Joined: 09 Apr 2018
Posts: 32
A 30-litre bucket contains a mixture of milk and water in the ratio 2:  [#permalink]

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Updated on: 05 Apr 2019, 04:25
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Difficulty:

55% (hard)

Question Stats:

67% (02:38) correct 33% (02:52) wrong based on 82 sessions

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A 30-litre bucket contains a mixture of milk and water in the ratio 2:1. A certain quantity of this mixture is replaced by water such that the ratio of milk and water becomes 8:7. This resultant mixture is added to 20 litres of another mixture containing milk and water in the ratio 3:1. What is the percentage of milk in the new mixture?

A 75%
B 53%
C 45%
D 62%
E 58%

Originally posted by lynnglenda on 05 Apr 2019, 03:19.
Last edited by Bunuel on 05 Apr 2019, 04:25, edited 1 time in total.
Renamed the topic.
Manager
Joined: 20 Oct 2018
Posts: 60
A 30-litre bucket contains a mixture of milk and water in the ratio 2:  [#permalink]

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Updated on: 06 Apr 2019, 09:41
1
1
Consider volume of milk = M and volume of water = W

Situation 1:
M/W=2/1
Let x denote the common factor: 2x+x=30
M = 20 and W=10

Situation 2:
Let us consider that "a" litres of solution has been replaced.
In "a" liters --> 2a/3 = milk and a/3 = water
M1= 20-2a/3
W1=10-(a/3)+a=10+(2a/3)
Note that we have replaced "a" liters of solution with water, hence "a" liters of water should be added
M1/W1=8/7
Solving this equation we get a=6
M1 = 16 and W1=14

Situation 3:
M2/W2=3/1
Let y be common factor: 3y+y=20
M2= 15 and W2=5

Total M = 16+15 = 31
Total W=14+5=19

Total M/Total(m+W) = 31/50 =62%

drakell thank you for noticing the mistake.

Originally posted by aniket16c on 06 Apr 2019, 06:50.
Last edited by aniket16c on 06 Apr 2019, 09:41, edited 1 time in total.
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Posts: 4
Re: A 30-litre bucket contains a mixture of milk and water in the ratio 2:  [#permalink]

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06 Apr 2019, 07:19
aniket16c wrote:
Consider volume of milk = M and volume of water = W

Situation 1:
M/W=2/1
Let x denote the common factor: 2x+x=30
M = 20 and W=10

Situation 2:
20/(10+x)=8/7 || x=15/2
M=20 and W = 35/2

Situation 3:
M2/W2=3/1
Let y be common factor: 3y+y=20
M2= 15 and W2=5

Total M = 20+15 = 35
Total W=35/2+5=45/2

Total M/Total(m+W) = 14/23 =62%

In situation 2, how is it possible for M to be the same as in the initial scenario? Volume of the milk is removed, and replaced with only water.
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Joined: 19 Jan 2017
Posts: 30
Location: India
Schools: IIM
GMAT 1: 530 Q48 V15
Re: A 30-litre bucket contains a mixture of milk and water in the ratio 2:  [#permalink]

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07 Apr 2019, 11:02
1
From first two sentences we can say that 30 ltr of water has 8:7 ratio.

8+7 =15 and 30/15= 2

Therefore final mixture has 16 ltr milk and 14 ltr water

In last sentence, we will follow the same process.

3+1=4, 20/4= 5
Therefore, new mixture contains 15 ltr of milk and 5 ltr of water

Total: 31 ltr milk and 19 ltr water
Total mixture 50 ltrs

31/50=62/100 ie 62 %

Posted from my mobile device
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Joined: 07 Dec 2014
Posts: 1222
A 30-litre bucket contains a mixture of milk and water in the ratio 2:  [#permalink]

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07 Apr 2019, 11:59
1
lynnglenda wrote:
A 30-litre bucket contains a mixture of milk and water in the ratio 2:1. A certain quantity of this mixture is replaced by water such that the ratio of milk and water becomes 8:7. This resultant mixture is added to 20 litres of another mixture containing milk and water in the ratio 3:1. What is the percentage of milk in the new mixture?

A 75%
B 53%
C 45%
D 62%
E 58%

let m=percentage of milk in new mixture
(8/15)(30)+(3/4)(20)=50m➡
m=31/50=62%
D
Intern
Joined: 28 Aug 2016
Posts: 11
Re: A 30-litre bucket contains a mixture of milk and water in the ratio 2:  [#permalink]

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14 Apr 2019, 17:23
lynnglenda wrote:
A 30-litre bucket contains a mixture of milk and water in the ratio 2:1. A certain quantity of this mixture is replaced by water such that the ratio of milk and water becomes 8:7. This resultant mixture is added to 20 litres of another mixture containing milk and water in the ratio 3:1. What is the percentage of milk in the new mixture?

A 75%
B 53%
C 45%
D 62%
E 58%

1). we have 20 liters of milk & 10 liters of water
2). 20-x/10+x = 8/7 , we can find x = 4. so now we have 16 liters of milk and 14 liters of water
3). we pour another 20 liters in a ratio 3:1, so we have another 15 liters milk and 5 liters water. Combining with the previous numbers:

16+15/ 14+5 = 31/19 -> looking for % of total: 31/50 or 62/ 100 -> 62%
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A 30-litre bucket contains a mixture of milk and water in the ratio 2:  [#permalink]

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23 May 2019, 10:21
Several litres of acid were drawn off a 54 L vessel full of acid and an equal amount of water added. Again, the same volume of the mixture was drawn off and replaced by water. As a result the vessel contained 24 L of pure acid. How much of the acid was drawn off initially?

A 30-litre bucket contains a mixture of milk and water in the ratio 2:   [#permalink] 23 May 2019, 10:21
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