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# A dishonest milk man tops up his bucket which is only 4/5 th full of m

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A dishonest milk man tops up his bucket which is only 4/5 th full of m  [#permalink]

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13 Jun 2016, 11:30
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55% (hard)

Question Stats:

65% (02:32) correct 35% (02:28) wrong based on 130 sessions

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A dishonest milk man tops up his bucket which is only 4/5 th full of milk with water. He again removes 5 liters of this mixture from the bucket and adds an equal quantity of water. If milk is now 60% of the mixture, what is the capacity of the bucket ?

A. 15 lit
B. 20 lit
C. 22.5 lit
D. 25 lit
E. 30 lit

Source : IIM Cat
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##### Most Helpful Community Reply
Intern
Joined: 06 Oct 2013
Posts: 45
A dishonest milk man tops up his bucket which is only 4/5 th full of m  [#permalink]

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Updated on: 15 Jun 2016, 13:25
2
3
msk0657 wrote:
A dishonest milk man tops up his bucket which is only 4/5 th full of milk with water. He again removes 5 liters of this mixture from the bucket and adds an equal quantity of water. If milk is now 60% of the mixture, what is the capacity of the bucket ?

A. 15 lit
B. 20 lit
C. 22.5 lit
D. 25 lit
E. 30 lit

Source : IIM Cat
_________________________________
Consider Kudos if helpful

Solution:

Let x be the capacity of the bucket.then, initial mixture has 80% milk.
then after 5 lt replaced with water---->$$(80/100)*(x-5)=(60/100)*x$$

x=20 lt.

Ans:- B.

Originally posted by AdlaT on 13 Jun 2016, 12:21.
Last edited by AdlaT on 15 Jun 2016, 13:25, edited 1 time in total.
##### General Discussion
Director
Joined: 20 Feb 2015
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Concentration: Strategy, General Management
Re: A dishonest milk man tops up his bucket which is only 4/5 th full of m  [#permalink]

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14 Jun 2016, 05:57
I would have plugged in the answer choices !!
for instance , if the capacity of the bucket = 20 litres
milk = 4/5=16 litres and water = 4 litres
he now removes 5 litres of this mixture , which is (4/5)*5 = 4 litres of milk
milk remaining = 16-4 = 12 litres = 60% of the solution .
Math Expert
Joined: 02 Aug 2009
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Re: A dishonest milk man tops up his bucket which is only 4/5 th full of m  [#permalink]

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14 Jun 2016, 06:23
msk0657 wrote:
A dishonest milk man tops up his bucket which is only 4/5 th full of milk with water. He again removes 5 liters of this mixture from the bucket and adds an equal quantity of water. If milk is now 60% of the mixture, what is the capacity of the bucket ?

A. 15 lit
B. 20 lit
C. 22.5 lit
D. 25 lit
E. 30 lit

Source : IIM Cat
_________________________________
Consider Kudos if helpful

Hi,

another way to look at the question....
when we are removing 5 litres of mix, it will contain
$$5*\frac{4}{5} = 4$$litre of milk.....
Now if capacity is x, $$\frac{4x}{5} - 4 = \frac{60x}{100} = \frac{3x}{5}.........\frac{4x}{5} - \frac{3x}{5}= 4...............x = 4*5 = 20$$

B
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 05 Dec 2015
Posts: 115
Re: A dishonest milk man tops up his bucket which is only 4/5 th full of m  [#permalink]

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21 Jun 2016, 21:34
AdlaT wrote:
msk0657 wrote:
A dishonest milk man tops up his bucket which is only 4/5 th full of milk with water. He again removes 5 liters of this mixture from the bucket and adds an equal quantity of water. If milk is now 60% of the mixture, what is the capacity of the bucket ?

A. 15 lit
B. 20 lit
C. 22.5 lit
D. 25 lit
E. 30 lit

Source : IIM Cat
_________________________________
Consider Kudos if helpful

Solution:

Let x be the capacity of the bucket.then, initial mixture has 80% milk.
then after 5 lt replaced with water---->$$(80/100)*(x-5)=(60/100)*x$$

x=20 lt.

Ans:- B.

Hello - great quick solution, do you mind explaining how you got the (x-5) portion of the equation. I'm having difficultly following the logic given the net amount of liquid is 0 (5 out, 5 in)

Thanks!
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Posts: 8527
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Re: A dishonest milk man tops up his bucket which is only 4/5 th full of m  [#permalink]

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21 Jun 2016, 22:23
msk0657 wrote:
A dishonest milk man tops up his bucket which is only 4/5 th full of milk with water. He again removes 5 liters of this mixture from the bucket and adds an equal quantity of water. If milk is now 60% of the mixture, what is the capacity of the bucket ?

A. 15 lit
B. 20 lit
C. 22.5 lit
D. 25 lit
E. 30 lit

Source : IIM Cat
_________________________________
Consider Kudos if helpful

You can also think of it as a weighted average question. Initial solution has 4/5th milk and 1/5th water so 80% milk. We remove 5 litres of this and put 5 litres of water (0% milk) instead. Overall, we get 60% milk solution.

Vol of 80% solution/ Vol of 0% milk solution = w1/w2 = (A2 - Aavg)/(Aavg - A1) = (0 - 60)/(60 - 80) = 3/1

Since volume of 0% milk solution (pure water) added was 5 lt, the 80% solution was 15 lt (after removal of 5 lt).

So original 80% solution was 15 + 5 = 20 lt

Answer (B)
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Senior Manager
Joined: 18 Jan 2010
Posts: 252
A dishonest milk man tops up his bucket which is only 4/5 th full of m  [#permalink]

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21 Jun 2016, 22:27
2
msk0657 wrote:
A dishonest milk man tops up his bucket which is only 4/5 th full of milk with water. He again removes 5 liters of this mixture from the bucket and adds an equal quantity of water. If milk is now 60% of the mixture, what is the capacity of the bucket ?

A. 15 lit
B. 20 lit
C. 22.5 lit
D. 25 lit
E. 30 lit

Milk : Water

$$\frac{4}{5}$$ :$$\frac{1}{5}$$

4: 1

say Milk is 4x, then water is x and total capacity of bucket is 5x.

when the vendor removes 5 L of the mixture, then because Milk and water are in the ratio 4:1, he will actually remove 4L milk and 1 L water.

So Now the bucket has:

Milk: 4x - 4
water: x-1

Now 5 L water is added. Bucket is now full.

Water volume: x-1+5

Milk : 4x-4
$$\frac{4x-4}{5x}$$ = 0.6

4x- 4 = 3x

x = 4.

Capacity = 5x = 20 Litres.

B is the answer
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Joined: 21 Jun 2016
Posts: 84
Location: India
Re: A dishonest milk man tops up his bucket which is only 4/5 th full of m  [#permalink]

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22 Jun 2016, 04:20
This was a difficult one for me. I used answer choice 20 and it worked out !
May be I should learn the right way to solve it.
Intern
Joined: 06 Oct 2013
Posts: 45
A dishonest milk man tops up his bucket which is only 4/5 th full of m  [#permalink]

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22 Jun 2016, 13:25
mdacosta wrote:
AdlaT wrote:
msk0657 wrote:
A dishonest milk man tops up his bucket which is only 4/5 th full of milk with water. He again removes 5 liters of this mixture from the bucket and adds an equal quantity of water. If milk is now 60% of the mixture, what is the capacity of the bucket ?

A. 15 lit
B. 20 lit
C. 22.5 lit
D. 25 lit
E. 30 lit

Source : IIM Cat
_________________________________
Consider Kudos if helpful

Solution:

Let x be the capacity of the bucket.then, initial mixture has 80% milk.
then after 5 lt replaced with water---->$$(80/100)*(x-5)=(60/100)*x$$

x=20 lt.

Ans:- B.

Hello - great quick solution, do you mind explaining how you got the (x-5) portion of the equation. I'm having difficultly following the logic given the net amount of liquid is 0 (5 out, 5 in)

Thanks!

x is the capacity of the bucket. In first sentence we are given that milk is only 4/5 capacity of the bucket =$$(80/100)*x$$.

In second sentence ,we are given that he replaced the 5 lt mixture with water, now milk percentage is $$80/100*(x-5)$$.

now the equation should look like this--->$$80/100*(x-5)+Percentage of the milk in water(which is 0)*5=60/100*(x-5+5)$$.

$$(80/100)*(x-5)+(0/100)*5=(60/100)*(x)---->(80/100)*(x-5)=(60/100)*x$$
VP
Joined: 07 Dec 2014
Posts: 1111
A dishonest milk man tops up his bucket which is only 4/5 th full of m  [#permalink]

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22 Jun 2016, 19:25
let c=capacity
look at water
.2c-.2*5+5=.4c
c=20 liters
Intern
Joined: 31 Dec 2017
Posts: 28
Concentration: Finance
Re: A dishonest milk man tops up his bucket which is only 4/5 th full of m  [#permalink]

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09 Feb 2018, 20:17
msk0657 wrote:
A dishonest milk man tops up his bucket which is only 4/5 th full of milk with water. He again removes 5 liters of this mixture from the bucket and adds an equal quantity of water. If milk is now 60% of the mixture, what is the capacity of the bucket ?

A. 15 lit
B. 20 lit
C. 22.5 lit
D. 25 lit
E. 30 lit

Source : IIM Cat
_________________________________
Consider Kudos if helpful

After filling the bucket with water: Milk - 4x/5, Water - 1x/5.

After removing 5 litres of mixture, quantity removed: Milk - 4, Water - 1
Resultant mixture = Milk: 4x/5 - 4, Water: x/5 - 1

After adding 5 litres of water, resultant mixture = Milk: 4x/5 - 4, Water: x/5 - 1 + 5

4x/5 - 4 = 0.6x
4x - 20/5 = 0.6x
4x - 20 = 3x
x = 20. (B).
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Joined: 31 May 2017
Posts: 321
Re: A dishonest milk man tops up his bucket which is only 4/5 th full of m  [#permalink]

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09 Feb 2018, 23:03
I solved by plugging in values.

Initial composition is 80/20. I chose the option B to verify.
20 liters = 16 liters of milk and 4 liters of water. Now remove 5 liters of the mixture, which by 80/20 mix ratio gives 4 lit milk/1 lit water.
Now we are left with 12 liters of milk and 8 liters of water. The milk is now 60% of mixture which matches the question stem.

Ans: B
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A dishonest milk man tops up his bucket which is only 4/5 th full of m  [#permalink]

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10 Feb 2018, 07:22
chetan2u wrote:
msk0657 wrote:
A dishonest milk man tops up his bucket which is only 4/5 th full of milk with water. He again removes 5 liters of this mixture from the bucket and adds an equal quantity of water. If milk is now 60% of the mixture, what is the capacity of the bucket ?

A. 15 lit
B. 20 lit
C. 22.5 lit
D. 25 lit
E. 30 lit

Source : IIM Cat
_________________________________
Consider Kudos if helpful

Hi,

another way to look at the question....
when we are removing 5 litres of mix, it will contain
$$5*\frac{4}{5} = 4$$litre of milk.....
Now if capacity is x, $$\frac{4x}{5} - 4 = \frac{60x}{100} = \frac{3x}{5}.........\frac{4x}{5} - \frac{3x}{5}= 4...............x = 4*5 = 20$$

B

Hello chetan2u,

why do you you assume when we subtract 5 litres of mixture from $$4/5$$ we get 4 litres of milk we subtract the the mixture of both water and milk from 4/5

why do you put x next to only 4 ? $$\frac{4x}{5}$$ shouldnt it be $$\frac{4x}{5x}$$

thank you
Math Expert
Joined: 02 Aug 2009
Posts: 7025
Re: A dishonest milk man tops up his bucket which is only 4/5 th full of m  [#permalink]

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10 Feb 2018, 07:42
1
dave13 wrote:
chetan2u wrote:
msk0657 wrote:
A dishonest milk man tops up his bucket which is only 4/5 th full of milk with water. He again removes 5 liters of this mixture from the bucket and adds an equal quantity of water. If milk is now 60% of the mixture, what is the capacity of the bucket ?

A. 15 lit
B. 20 lit
C. 22.5 lit
D. 25 lit
E. 30 lit

Source : IIM Cat
_________________________________
Consider Kudos if helpful

Hi,

another way to look at the question....
when we are removing 5 litres of mix, it will contain
$$5*\frac{4}{5} = 4$$litre of milk.....
Now if capacity is x, $$\frac{4x}{5} - 4 = \frac{60x}{100} = \frac{3x}{5}.........\frac{4x}{5} - \frac{3x}{5}= 4...............x = 4*5 = 20$$

B

Hello chetan2u,

Quote:
why do you you assume when we subtract 5 litres of mixture from $$4/5$$ we get 4 litres of milk we subtract the the mixture of both water and milk from 4/5

milk is 4/5 of total which means in 5x litres, 4x are milk and 1x is water
so when we take out 5 litres and when both milk and water are mixed in that ratio 4:(5-1), 4 litres taken out is milk and 1 is water

Quote:
why do you put x next to only 4 ? $$\frac{4x}{5}$$ shouldnt it be $$\frac{4x}{5x}$$

thank you

4x/5x will be used when I say there are 5x litres and 4x is milk out of it..
But here I am taking x as total MIX and 4/5 of total is milk, therefore $$\frac{4}{5} * x = \frac{4x}{5}$$
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: A dishonest milk man tops up his bucket which is only 4/5 th full of m &nbs [#permalink] 10 Feb 2018, 07:42
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