Mixing two alloys in equal weights — Aptitude Question
Mixing two alloys in equal weights: One alloy has copper and zinc in the ratio 5 : 3, another in the ratio 7 : 5. Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 120 seconds
Question
One alloy has copper and zinc in the ratio 5 : 3, another in the ratio 7 : 5. Equal weights of the two are melted together. What is the ratio of copper to zinc in the new alloy?
Options
- 12 : 8
- 23 : 19
- 29 : 19
- 35 : 15
Show the answer and the worked solution
Correct answer: C. 29 : 19
Worked solution
- Take 24 units of each (24 divides both 8 and 12).
- First alloy: copper 15, zinc 9. Second: copper 14, zinc 10.
- Totals: copper 29, zinc 19 → 29 : 19.
Answer: 29 : 19.
The idea
Choose a common weight that both ratios divide cleanly — the LCM of the ratio sums — then add the components. Averaging the two ratios directly is wrong.
Shortcut. Copper is 5/8 = 15/24 of one alloy and 7/12 = 14/24 of the other; equal weights give 29 copper out of 48, so zinc is 19: 29 : 19.
Common trap. "12 : 8" — adding the ratio terms (5 + 7 : 3 + 5), which weights the alloys unequally because one is split into 8 parts and the other into 12.