Combining two wine–water mixtures and adding extra water: Cask 1 has 48 L with wine:water = 13 : 7. Cask 2 has 42 L with wine:water = 18 : 17. After mixing their contents and adding 20 L of water, what is the final wine:water ratio?

Introduction / Context: Convert ratios to absolute amounts using the given volumes, then add the wine and water from both casks. Finally add 20 L water and reduce the resulting wine:water pair to the simplest integer ratio.

Given Data / Assumptions:

• Cask 1 (48 L): wine = 13/20*48 = 31.2 L; water = 16.8 L.
• Cask 2 (42 L): wine = 18/35*42 = 21.6 L; water = 20.4 L.
• Extra water added = 20 L.

Concept / Approach: Sum wine and water separately, then express as a reduced ratio. The added water changes only the denominator (water amount), not wine.

Step-by-Step Solution:

Verification / Alternative check: Divide both by 44: 528/44 = 12; 572/44 = 13, so the ratio simplifies cleanly.

Why Other Options Are Wrong: 13 : 12 is the inverse; 21 : 31 and 31 : 21 are unrelated to the computed totals.

Common Pitfalls: Averaging ratios directly; always compute actual amounts before reducing to a ratio.

Final Answer: 12 : 13