Alligation–Mixture (Two Acid–Water Solutions):\nTwo bottles have acid:water ratios 2:3 and 1:2, respectively. Mixed in the ratio 1:3 (by volume), what is the final acid:water ratio?

Introduction / Context:
Combining solutions requires adding absolute component amounts, not averaging ratios.

Given Data / Assumptions:

• Bottle A (2:3), Bottle B (1:2).
• Volumes mixed A:B = 1:3.

Concept / Approach:
Let A = 1 unit, B = 3 units. Compute acid and water separately, then form the ratio.

Step-by-Step Solution:
1) Acid from A = 1*(2/5) = 2/5; water from A = 3/5.2) Acid from B = 3*(1/3) = 1; water from B = 3*(2/3) = 2.3) Total acid = 2/5 + 1 = 7/5; total water = 3/5 + 2 = 13/5 ⇒ ratio 7:13.

Verification / Alternative check:
Divide both totals by 1/5 to see integer ratio 7:13.

Why Other Options Are Wrong:
They arise from averaging ratios or mixing numeric errors.

Common Pitfalls:
Taking arithmetic means of ratios—never valid for mixture composition.

Final Answer:
7:13