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Two vessels contain milk and water in the ratio of 7:3 and 2:3 respectively. Find the ratio in which the contents of both the vessels must be mixed to get a new mixture containing milk and water  in the ratio 3:2.
  • a)
    2:1
  • b)
    2:3
  • c)
    3:1
  • d)
    3:5
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Two vessels contain milk and water in the ratio of 7:3 and 2:3 respect...
Answer – a) 2:1 Explanation : let the ratio be k:1 then in first mixture, milk = 7k/10 and water = 3k/10 and in second mixture, milk = 2/5 and water = 3/5 [7k/10 + 2/5]/[3k/10 3/5] = 3/2 K = 2, so ratio will be 2:1
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Two vessels contain milk and water in the ratio of 7:3 and 2:3 respect...
Problem: Two vessels contain milk and water in the ratio of 7:3 and 2:3 respectively. Find the ratio in which the contents of both the vessels must be mixed to get a new mixture containing milk and water in the ratio 3:2.

Solution:

Let the quantity of milk and water in the first vessel be 7x and 3x respectively.

Let the quantity of milk and water in the second vessel be 2y and 3y respectively.

Now, we need to find the ratio in which the contents of both the vessels must be mixed to get a new mixture containing milk and water in the ratio 3:2.

Let us assume that we take x units from the first vessel and y units from the second vessel.

The quantity of milk in the new mixture = 7x/10 + 2y/5

The quantity of water in the new mixture = 3x/10 + 3y/5

According to the question, the ratio of milk and water in the new mixture is 3:2.

Therefore,

(7x/10 + 2y/5)/(3x/10 + 3y/5) = 3/2

Simplifying this equation, we get:

14x + 12y = 45x

31x = 12y

x/y = 12/31

Therefore, the ratio in which the contents of both the vessels must be mixed to get a new mixture containing milk and water in the ratio 3:2 is 12:31.

Hence, the correct answer is option 'A' (2:1).
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