A bucket contains a mixture of two liquids A and B in the ratio 7 : 5. Then 9 litres of this mixture is removed and replaced by 9 litres of pure liquid B.\nAfter this replacement, the ratio of liquid A to liquid B becomes 7 : 9.\nHow many litres of liquid A were originally present in the bucket?

Introduction:
This is a replacement mixture question where part of a mixture is removed and replaced with one component. The key is to express initial quantities using a total volume variable, compute how much A and B are removed with the 9 litres mixture, then add back 9 litres of pure B, and finally use the new ratio to solve for the initial total and initial A quantity.

Given Data / Assumptions:

• Initial ratio A : B = 7 : 5
• 9 litres of mixture removed
• 9 litres of pure B added
• New ratio A : B = 7 : 9
• Let initial total mixture = V litres

Concept / Approach:
Initial A = (7/12)V and initial B = (5/12)V.\nWhen 9 litres are removed, A removed = 9*(7/12) and B removed = 9*(5/12).\nThen add 9 litres of B only. Use the final ratio to solve for V, then compute initial A.

Step-by-Step Solution:
Let initial total = VInitial A = (7/12)V, Initial B = (5/12)VA removed = 9 * (7/12) = 63/12 = 21/4B removed = 9 * (5/12) = 45/12 = 15/4A after removal = (7/12)V - 21/4B after removal = (5/12)V - 15/4Add 9 litres of B: B becomes (5/12)V - 15/4 + 9 = (5/12)V + 21/4Final ratio condition: [(7/12)V - 21/4] : [(5/12)V + 21/4] = 7 : 9Solve gives V = 36 litresInitial A = (7/12) * 36 = 21 litres

Verification / Alternative Check:
With V = 36: initial A = 21, B = 15. Remove 9 litres mixture (ratio 7:5) removes A = 5.25 and B = 3.75. Left: A = 15.75, B = 11.25. Add 9 litres B: B = 20.25. Ratio A:B = 15.75:20.25 = 7:9 after dividing by 2.25, correct.

Why Other Options Are Wrong:
15 or 18 litres: would not produce the exact new ratio after replacement.23 or 24 litres: makes A too high relative to B in the final mixture.

Common Pitfalls:
Assuming 9 litres removed is only A or only B, instead of a mixture.Forgetting to add back 9 litres of pure B after removal.Not expressing initial quantities using a total volume variable.

Final Answer:
21 litres