Alloys mixed: 4 kg of an alloy with 1/4 iron (rest tin) is blended with 6 kg of another alloy with 2/3 iron (rest tin). Find the iron : tin ratio in the final mixture.

Introduction / Context: When mixing alloys, compute the actual masses of each component (iron and tin) from each alloy, then add them to obtain totals and simplify to a ratio. This problem uses simple fractions of iron in each alloy.

Given Data / Assumptions:

• Alloy 1: 4 kg with iron fraction 1/4 ⇒ iron 1 kg, tin 3 kg.
• Alloy 2: 6 kg with iron fraction 2/3 ⇒ iron 4 kg, tin 2 kg.

Concept / Approach: Add iron masses and tin masses separately: iron_total = iron1 + iron2; tin_total = tin1 + tin2. Express as iron : tin and reduce if possible.

Step-by-Step Solution: Iron_total = 1 + 4 = 5 kg. Tin_total = 3 + 2 = 5 kg. Therefore, iron : tin = 5 : 5 = 1 : 1.

Verification / Alternative check: The totals sum to 10 kg, matching the combined mass. Equal iron and tin indicate a balanced mixture.

Why Other Options Are Wrong: 2 : 1, 1 : 2, 3 : 2 do not match the computed component totals for this specific mixing.

Common Pitfalls: Confusing “fraction of iron” with “fraction of tin” or failing to multiply by the mass of each alloy before adding.

Final Answer: 1 : 1