Replacing mixture with pure component changes ratio: A can initially has liquids A and B in the ratio 7 : 5. After drawing off 9 L of the mixture and refilling with pure B, the ratio becomes 7 : 9. How many liters of A were in the can originally?

Introduction / Context:
When a fixed volume of a mixture is removed, each component is reduced proportionally. Adding back pure B increases B only. Using initial ratio parts and total volume lets us model the new amounts and match the final ratio to solve for the scale factor and the initial amount of A.

Given Data / Assumptions:

• Initial A : B = 7 : 5 ⇒ A0 = 7k, B0 = 5k, total = 12k.
• Draw off 9 L; refill with 9 L of pure B.
• Final A : B = 7 : 9.

Concept / Approach:
After drawing 9 L, remaining fraction = 1 − 9/(12k). Thus A1 = 7k*(1 − 9/(12k)); B1 = 5k*(1 − 9/(12k)) + 9. Set A1/B1 = 7/9 and solve for k, then compute A0 = 7k.

Step-by-Step Solution:

Verification / Alternative check:
Total 12k = 36 L; removing 9 L leaves 27 L; adding 9 L B restores 36 L. Final A : B computed equals 7 : 9 as required.

Why Other Options Are Wrong:
They do not satisfy the transformed ratio equation after removal and refill.

Common Pitfalls:
Subtracting 9 L directly from A and B parts instead of reducing them proportionally to total.

Final Answer:
21 L