Numerical answer
Alloy X contains gold and copper in the ratio 5 : 3, and alloy Y contains them in the ratio 7 : 5. How many kilograms of alloy X must be melted with 36 kg of alloy Y to obtain an alloy in which gold and copper are in the ratio 3 : 2?
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Answer: 24
Work with the fraction of gold: X = 5/8 = 0.625, Y = 7/12 ≈ 0.5833, target = 3/5 = 0.6.
Alligation: X : Y = (0.6 − 7/12) : (5/8 − 0.6) = (1/60) : (1/40) = 2 : 3.
With 36 kg of Y, X = 36 × 2/3 = 24 kg.
Check: gold = 24 × 5/8 + 36 × 7/12 = 15 + 21 = 36; total 60 → 36/60 = 3/5 ✓.
Alligation: X : Y = (0.6 − 7/12) : (5/8 − 0.6) = (1/60) : (1/40) = 2 : 3.
With 36 kg of Y, X = 36 × 2/3 = 24 kg.
Check: gold = 24 × 5/8 + 36 × 7/12 = 15 + 21 = 36; total 60 → 36/60 = 3/5 ✓.
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