Mixture and Alligation: A can contain a mixture of two liquids A and B in the ratio 7:5. When 9 liters of mixture is replaced by liquid B, the ratio becomes 7:9. Find the quantity of liquid A in the original mixture.

Let total quantity of mixture = x liters

Initial ratio of A : B = 7 : 5

→ A = (7/12) × x

→ B = (5/12) × x

Now, 9 liters of mixture is removed and replaced with 9 liters of liquid B.

Amount of A removed = (7/12) × 9 = 5.25 liters

Amount of B removed = (5/12) × 9 = 3.75 liters

New quantity of A = (7/12)x − 5.25

New quantity of B = (5/12)x − 3.75 + 9 = (5/12)x + 5.25

New ratio:

[(7/12)x − 5.25] / [(5/12)x + 5.25] = 7 / 9

Cross-multiply:

9[(7/12)x − 5.25] = 7[(5/12)x + 5.25]

→ 9 × (7x − 63)/12 = 7 × (5x + 63)/12

→ 63x − 567 = 35x + 441

→ 28x = 1008

→ x = 36

So, original quantity of liquid A = (7/12) × 36 = 21 liters