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Two liquids A and B are in the ratio 4 : 3 in container X and 2 : 5 in container Y. In what ratio should the content of both container be mixed so that the resulting mixture has A and B in ratio 3 : 5.
  • a)
    5:11
  • b)
    4:13
  • c)
    2:11
  • d)
    7:15
Correct answer is option 'A'. Can you explain this answer?
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Two liquids A and B are in the ratio 4 : 3 in container X and 2 : 5 in...
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Two liquids A and B are in the ratio 4 : 3 in container X and 2 : 5 in...
Solution:

Let the container X have 4x units of liquid A and 3x units of liquid B.

Let the container Y have 2y units of liquid A and 5y units of liquid B.

Now, we need to find the ratio in which the contents of both containers should be mixed so that the resulting mixture has A and B in the ratio 3:5.

Let the ratio be a:b.

Then, the amount of liquid A in the mixture will be (4x*a/7x) + (2y*b/7y) and the amount of liquid B in the mixture will be (3x*a/7x) + (5y*b/7y).

According to the question,

(4x*a/7x) + (2y*b/7y) : (3x*a/7x) + (5y*b/7y) = 3:5

Multiplying both sides by 7/2, we get

(2a + b)/(3a + 5b) = 21/10

Solving for a/b, we get

a/b = 5/11

Therefore, the ratio in which the contents of both containers should be mixed so that the resulting mixture has A and B in ratio 3:5 is 5:11.
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Two liquids A and B are in the ratio 4 : 3 in container X and 2 : 5 in container Y. In what ratio should the content of both container be mixed so that the resulting mixture has A and B in ratio 3 : 5.a)5:11b)4:13c)2:11d)7:15Correct answer is option 'A'. Can you explain this answer?
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