A bucket contains a mixture of two liquids A and B in the proportion 7: 5. If 9 litres of the mixture is replaced by 9 litres of liquid B, then the ratio of the two liquid becomes 7: 9. How much of the liquid A was there in the bucket?

Step 1: Let the total quantity of the mixture be x litres.

• Initial ratio of A : B = 7 : 5
• So, quantity of A = (7/12) × x
• Quantity of B = (5/12) × x

Step 2: 9 litres of the mixture is removed

• Since the ratio is 7:5, amount of A removed = (7/12) × 9 = 5.25 litres
• Amount of B removed = (5/12) × 9 = 3.75 litres

Step 3: 9 litres of B is added back

• New amount of A = (7/12)x - 5.25
• New amount of B = (5/12)x - 3.75 + 9 = (5/12)x + 5.25
• New ratio = 7 : 9

Step 4: Set up the ratio equation

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

Step 5: Cross-multiply to solve

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

(63/12)x - 47.25 = (35/12)x + 36.75

Step 6: Solve for x

(63/12)x - (35/12)x = 36.75 + 47.25
(28/12)x = 84
(7/3)x = 84
x = (84 × 3) / 7 = 252 / 7 = 36 litres

Step 7: Find quantity of liquid A

Liquid A = (7/12) × 36 = 21 litres

Answer: 21 litres

There were 21 litres of liquid A in the bucket originally.