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

Question

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

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

Source : IIM Cat

adiagr · Accepted Answer

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

AdlaT · Answer

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.

CounterSniper · Answer

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 .

chetan2u · Answer

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

mdacosta · Answer

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!

KarishmaB · Answer

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)

HMC · Answer

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.

AdlaT · Answer

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

gracie · Answer

let c=capacity
look at water
.2c-.2*5+5=.4c
c=20 liters

mbafinhopeful · Answer

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).

akadiyan · Answer

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

dave13 · Answer

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

chetan2u · Answer

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

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}

youcouldsailaway · Answer

I used the multiple replacement method to solve this question.

\(C_{final} = C_{initial} ( \frac{V_i }{ V}) ^ n\)

where,

\(C_{final}\) = final concentration of the element that was not added back (here, milk)
\(C_{initial}\) = initial concentration of the element that was not added back (here, milk)
\(V_i\) = Total volume after initial removal of some part of the mixture (here, V-5)
\(V\) = Beginning volume before removal of some part of the mixture (here, V)
\(n\) = total replacements

\(\frac{3}{5} = \frac{4}{5} (\frac{V-5 }{ V}) ^1\)

V = 20 L

Method better explained here: https://gmatclub.com/forum/two-importan ... 82701.html

Bungi · Answer

To solve this problem, we need to set up an equation based on the given information. Let's assume the capacity of the bucket is 'x' liters.

According to the problem, the dishonest milkman tops up his bucket, which is only 4/5 full of milk, with water. This means there is 4/5 of milk and 1/5 of water in the bucket after the first operation.

Next, the milkman removes 5 liters of this mixture from the bucket and replaces it with an equal quantity of water. This means that the amount of milk in the bucket remains the same, but the total quantity of the mixture increases by 5 liters.

Now, we are given that after these operations, the milk is 60% of the mixture. This means that the milk accounts for 60% of the total quantity of the mixture, while the water accounts for the remaining 40%.

Based on this information, we can set up the equation:

(4/5)x = 0.6(x + 5)

Let's solve this equation to find the value of 'x', which represents the capacity of the bucket.

Multiplying both sides of the equation by 5 to eliminate the fraction, we get:

4x = 0.6x + 3

Subtracting 0.6x from both sides, we get:

4x - 0.6x = 3

Simplifying, we have:

3.4x = 3

Dividing both sides by 3.4, we find:

x = 3 / 3.4

Calculating this, we get:

x ≈ 0.8824

Therefore, the capacity of the bucket is approximately 0.8824 liters.

nirajkr · Answer

To solve quickly 
I would have gone for a removed mixture of 5l
5l removed means 4l milk and 1l water
again 5l water added to the new mixture 
so exchanging 4l milk with 4l water => reduces milk concentration from 80% to 60%
Therefore, 4l translates to 20% of the capacity of the bucket

So, for 100% the bucket capacity will be 4*5 = 20l

Option B

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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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