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A vessel contains a mixture of liquid A and liquid B in the ratio 3 : 2. Five litres of mixture are taken out and replaced by liquid B. Thereafter, the ratio of liquid A and liquid B becomes 2 : 3. Find the quantity of liquid A in the mixture initially.
  • a)
    1 Ltr.
  • b)
    2 Ltr
  • c)
    9 Ltr
  • d)
    4 Ltr
  • e)
    5 Ltr
Correct answer is option 'C'. Can you explain this answer?
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A vessel contains a mixture of liquid A and liquid B in the ratio 3 : ...
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A vessel contains a mixture of liquid A and liquid B in the ratio 3 : ...
Given:
- The ratio of liquid A and liquid B in a mixture = 3:2
- 5 litres of mixture taken out and replaced with liquid B
- The new ratio of A and B = 2:3

To find: The quantity of liquid A in the mixture initially

Solution:
Let's assume the initial quantity of liquid A in the mixture = 3x and the initial quantity of liquid B = 2x
So, the total initial quantity of the mixture = 3x+2x = 5x

When 5 litres of mixture is taken out, the quantity of liquid A and liquid B in the mixture becomes:

- Liquid A = 3x - (3/5) × 5x = 3x - 3x = 0
- Liquid B = 2x - (2/5) × 5x + 5 = 2x - 2x + 5 = 5

After the replacement, the ratio of A and B becomes 2:3. Therefore, we can write:

- Liquid A/Liquid B = 2/3

Substituting the values:

- 3x/5 = 2/3
- x = 5

So, the initial quantity of liquid A = 3x = 3 × 5 = 15 litres

Therefore, the quantity of liquid A in the mixture initially is 15 litres.

Hence, the correct answer is option (c).
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A vessel contains a mixture of liquid A and liquid B in the ratio 3 : 2. Five litres of mixture are taken out and replaced by liquid B. Thereafter, the ratio of liquid A and liquid B becomes 2 : 3. Find the quantity of liquid A in the mixture initially.a)1 Ltr.b)2 Ltrc)9 Ltrd)4 Ltre)5 LtrCorrect answer is option 'C'. Can you explain this answer?
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