Two bottles contain acid and water in the ratios 2:3 and 1:2 respectively (acid:water). These two mixtures are mixed together in the ratio 1:3 (first mixture : second mixture). What is the ratio of acid to water in the final mixture?

Introduction / Context:
This question tests compound mixture calculation. Each bottle has its own internal composition (acid fraction and water fraction). When you mix the two bottles in a given external ratio, you must scale the acid and water contributions accordingly and then add them. The final ratio is based on total acid and total water, not on any single bottle ratio. The safest method is to assume convenient volumes (like 1 litre and 3 litres) matching the mixing ratio.

Given Data / Assumptions:

• Mixture 1 acid:water = 2:3
• Mixture 2 acid:water = 1:2
• Mixed in ratio (Mixture 1 : Mixture 2) = 1:3
• Assume 1 litre of mixture 1 and 3 litres of mixture 2

Concept / Approach:
Convert each ratio to fractions. For 2:3, total parts 5, acid fraction = 2/5, water fraction = 3/5. For 1:2, total parts 3, acid fraction = 1/3, water fraction = 2/3. Multiply fractions by assumed litres, add totals, and simplify the final ratio.

Step-by-Step Solution:
Take 1 litre of mixture 1 and 3 litres of mixture 2 Mixture 1: acid = (2/5)*1 = 2/5, water = (3/5)*1 = 3/5 Mixture 2: acid = (1/3)*3 = 1, water = (2/3)*3 = 2 Total acid = 2/5 + 1 = 7/5 Total water = 3/5 + 2 = 13/5 Final ratio acid:water = (7/5):(13/5) = 7:13

Verification / Alternative check:
You can also convert both totals to the same denominator and confirm the denominator cancels. The result 7:13 remains stable no matter what base litres you assume, as long as you keep the 1:3 mixing ratio.

Why Other Options Are Wrong:
1:3 ignores internal compositions and wrongly assumes mixture 2 dominates as if it were pure water. 23:37 and 11:57 come from incorrect fraction conversion (like using 2/3 instead of 2/5). 5:9 does not match the computed acid and water totals.

Common Pitfalls:
Using 2:3 as acid fraction 2/3 instead of 2/5, forgetting to multiply mixture 2 contributions by 3, or reversing the external mixing ratio 1:3 as 3:1.

Final Answer:
The ratio of acid to water in the final mixture is 7:13.