How to Solve Alloy and Metal Mixture Problems
Solve alloy and metal mixture problems using weight-based percentages and alligation, with a worked example and practice questions with answers.
Expected Interview Answer
Alloy problems treat each metal as a fraction of total weight, the same way liquid mixture problems treat volume, so an alloy that is X% copper by weight contains X% of its total mass as copper, and combining two alloys means adding each metal’s actual weight separately before recomputing percentages.
The setup mirrors mixture problems exactly: given an alloy’s total weight and its metal composition as a ratio or percentage, multiply to get each metal’s weight. When two alloys of different compositions are melted together, add the weight of each metal across both alloys, then divide by the new combined total weight to get the new percentage composition — never average the two original percentages directly, since that ignores the different total weights. Alligation applies directly when the problem asks “in what ratio should two alloys be mixed to get a target percentage,” treating the two alloys’ metal percentages as the two “prices” in the alligation cross. Watch for problems that ask for weight added of pure metal, which is a special case where one “alloy” is 100% pure.
- Percentage-of-weight framing unifies alloy problems with liquid mixtures
- Alligation directly solves “mix two alloys to hit a target percentage” questions
- Treating pure metal as a 100% alloy handles addition-of-pure-metal cases cleanly
AI Mentor Explanation
A 30-player squad is 60% experienced (18 players) by headcount; merging with a second 20-player squad that is 40% experienced (8 players) gives a combined 28 experienced players out of 50 total, or 56% — found by adding the actual experienced-player counts, not by averaging 60% and 40% directly, since the squads have different sizes. This weight-of-metal-not-percentage-averaging principle is exactly how two alloys are correctly combined.
Worked example (combining two alloys)
Alloy A copper
- 30% of 40kg = 12kg
Alloy B copper
- 60% of 60kg = 36kg
Combined percentage
- 48kg / 100kg = 48%
Step-by-Step Explanation
Step 1
Convert percentage to weight
Multiply each alloy’s total weight by its metal percentage to get the metal weight.
Step 2
Add weights when combining
Sum each metal’s actual weight and the total weight separately across alloys.
Step 3
Recompute the new percentage
New percentage = combined metal weight ÷ combined total weight.
Step 4
Use alligation for a target ratio
To hit a target percentage by mixing two alloys, apply the alligation cross-difference ratio.
What Interviewer Expects
- Correct conversion between percentage and metal weight
- Adding actual weights, not averaging percentages, when combining alloys
- Correct recomputation of the new percentage after combining
- Applying alligation for target-ratio alloy mixing questions
Common Mistakes
- Averaging two alloy percentages directly, ignoring different total weights
- Forgetting to convert percentages to actual metal weights before adding
- Treating pure metal addition as a percentage blend rather than a 100% alloy case
- Misapplying alligation without first identifying which is the “cheaper” and “dearer” percentage
Best Answer (HR Friendly)
“I treat each alloy like a mixture problem — convert the percentage composition into an actual metal weight by multiplying by the total weight. When combining two alloys, I add the actual metal weights and the actual total weights separately, then divide to get the new percentage — I never average the two percentages directly, because that ignores the alloys having different masses. If the question asks for a mixing ratio to hit a target percentage, that is a direct alligation setup with the two percentages as the two prices.”
Follow-up Questions
- How do you solve for the amount of pure metal to add to reach a target percentage?
- How does this differ when the alloy loses weight during melting (wastage)?
- How would you solve a three-metal alloy composition problem?
- How is adding pure metal treated differently from combining two alloys?
MCQ Practice
1. Alloy A weighs 50kg and is 20% zinc. Alloy B weighs 50kg and is 40% zinc. What is the zinc percentage in the combined alloy?
Zinc: 10kg + 20kg = 30kg out of 100kg total = 30%.
2. How much pure copper (100%) must be added to 20kg of an alloy that is 30% copper, to make it 50% copper?
Using alligation with values 30% and 100%, target 50%: ratio existing:pure = (100−50):(50−30) = 50:20 = 5:2. Existing 20kg = 5 parts, so 1 part = 4kg, and pure copper = 2 parts = 8kg.
3. In what ratio should a 25% tin alloy be mixed with a 65% tin alloy to get a 45% tin alloy?
Alligation ratio = (65−45):(45−25) = 20:20 = 1:1.
Flash Cards
How to find metal weight from a percentage? — Metal weight = alloy total weight × metal percentage.
How to combine two alloys correctly? — Add actual metal weights and total weights separately, then recompute the percentage — never average percentages directly.
When does alligation apply to alloys? — When mixing two alloys of known percentages to hit a target percentage.
How is adding pure metal treated? — As a special alligation case where one “alloy” is 100% pure.