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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 has sold. What is the current proportion of water to milk?  
  • a)
    2 : 3
  • b)
    1 : 2
  • c)
    1 : 3
  • d)
    3 : 4
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A milkman mixes 20 litres of water with 80 litres of milk. After selli...
Given information:
A milkman mixes 20 litres of water with 80 litres of milk.

Solution:
Let's assume that the initial proportion of water to milk is x : y.
So, the initial quantity of water = 20 litres and the initial quantity of milk = 80 litres, then we can write:

20/x = 80/y

=> y/x = 4/1

=> y = 4x

Now, the milkman sells 1/4 of the mixture, which means he sells 25% of the mixture.

Quantity sold = 25% of (20 + 80) litres = 25% of 100 litres = 25 litres

After selling, the remaining mixture contains 20 + 80 - 25 = 75 litres.

Now, the milkman adds water to replenish the quantity that he has sold. Let's assume that he adds 'a' litres of water.

Therefore, the new quantity of water = 20 + a litres and the new quantity of milk = 80 litres.

The new proportion of water to milk can be written as:

(20 + a)/x : 80/y

=> (20 + a)/x : 80/(4x) (as y = 4x)

=> (20 + a)/x : 20/x

=> (20 + a)/20

Now, we know that the quantity sold was 25 litres, which means the new quantity of milk after replenishing will be 75 litres.

So, the new proportion of water to milk can be written as:

(20 + a)/20 : 75/80

=> (20 + a)/20 : 3/4

We need to find the current proportion of water to milk, which means we need to find the value of 'a' such that the above proportion becomes 2:3.

(20 + a)/20 : 3/4 = 2/3

Cross-multiplying, we get:

(20 + a)*3 = 2*20*4

=> 60 + 3a = 160

=> a = 33.33 litres

Therefore, the current proportion of water to milk is:

(20 + 33.33)/20 : 75/80

=> 2.17 : 3

Rounding off, we get:

2 : 3

Hence, the correct answer is option A.
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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 has sold. What is the current proportion of water to milk?a)2 : 3b)1 : 2c)1 : 3d)3 : 4Correct answer is option 'A'. Can you explain this answer?
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