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A solution contains a mixture of liquid A and B in the ratio of 3 : 2. When 10 litre of solution is taken out and replaced by 10 litre of liquid B, the ratio of liquids A and B in the new solution is 1 : 2. What was the volume of the initial solution?
  • a)
    30 litres
  • b)
    22 litres
  • c)
    20 litres
  • d)
    22.5 litres
  • e)
    24 litres
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A solution contains a mixture of liquid A and B in the ratio of 3 : 2....
Let's assume that the initial volume of the solution is 'x' liters.

Given that the ratio of liquid A to liquid B in the initial solution is 3:2, we can calculate the volumes of liquid A and B in the initial solution as follows:
Volume of liquid A = (3/5) * x
Volume of liquid B = (2/5) * x

After removing 10 liters of the solution, the volume of liquid A remaining in the solution is:
Volume of liquid A remaining = (3/5) * x - (3/5) * 10

After adding 10 liters of liquid B, the volume of liquid B in the new solution is:
Volume of liquid B = (2/5) * x + 10

Given that the ratio of liquid A to liquid B in the new solution is 1:2, we can equate the volumes of liquid A and B in the new solution and solve for 'x'.

Equating the volumes of liquid A and B in the new solution:
(3/5) * x - (3/5) * 10 = (2/5) * x + 10

Simplifying the equation:
(3/5) * x - (2/5) * x = 10 + (3/5) * 10
x/5 = 10 + 6
x/5 = 16
x = 80

Therefore, the initial volume of the solution is 80 liters.

Hence, the correct answer is option D) 80 liters.
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