A container holds a mixture of liquid A and liquid B in the ratio 7 : 5. After 9 litres of this mixture are removed and the container is refilled with pure liquid B, the proportion of A to B changes to 7 : 9. Determine the initial quantity of liquid A present in the container.
Show answer & explanation
Correct answer: D
Explanation
Given:
A : B = 7 : 5
Mixture drawn = 9 liters
New ratio = 7 : 9
Formula:
A and B are added to the mixture in the same ratio.
Let the total mixture = 12x
A = 7x
B = 5x
9 liters drawn
A = (7/12) × 9 = 5.25
B = (5/12) × 9 = 3.75
Remaining A = 7x − 5.25
Remaining B = 5x − 3.75
9 liters of pure B added
New B = 5x − 3.75 + 9 = 5x + 5.25
New ratio
(7x − 5.25) / (5x + 5.25) = 7 / 9
9(7x − 5.25) = 7(5x + 5.25)
63x − 47.25 = 35x + 36.75
28x = 84
x = 3
Initial A = 7x = 21 liters