Two vessels poured together — Aptitude Question
Two vessels poured together: Two vessels of equal capacity hold milk and water in the ratios 5 : 3 and 5 : 7. Answer and worked solution on CodeKairo.
- Topic: Mixtures & Alligation
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
Two vessels of equal capacity hold milk and water in the ratios 5 : 3 and 5 : 7. Their contents are poured into a third vessel. What is the new ratio?
Options
- 25 : 21
- 25 : 23
- 5 : 4
- 12 : 11
Show the answer and the worked solution
Correct answer: B. 25 : 23
Worked solution
- Take 24 L from each vessel (24 divides both 8 and 12).
- First: milk 15, water 9. Second: milk 10, water 14.
- Totals: milk 25, water 23 → 25 : 23.
Answer: 25 : 23.
The idea
Choose a common volume that both ratio sums divide — the LCM of 8 and 12 is 24. Averaging the ratios directly is always wrong.
Shortcut. The milk fractions 5/8 and 5/12 average to (30 + 20)/96 = 25/48, so water is 23/48: 25 : 23.
Common trap. 5 : 4 — scaling the first vessel to 24 L (15 : 9) but adding the second unscaled as 5 : 7, giving 20 : 16; equal capacity means equal volumes.