Single correct option
Alloy X contains copper and zinc in the ratio 3 : 2, and alloy Y contains them in the ratio 2 : 1. In what ratio (by weight) must X and Y be mixed so that the resulting alloy has copper and zinc in the ratio 5 : 3?
- A. 3 : 5
- B. 2 : 1
- C. 5 : 3
- D. 4 : 3
Show answer and solution
Answer: (C) 5 : 3
Copper fraction: X = 3/5 = 0.6, Y = 2/3 ≈ 0.667, target = 5/8 = 0.625.
By alligation, X : Y = (2/3 − 5/8) : (5/8 − 3/5) = (1/24) : (1/40) = 40 : 24 = 5 : 3.
Check: 5 kg of X gives 3 kg copper, 3 kg of Y gives 2 kg copper; total 5 kg copper in 8 kg = 5/8. ✓
Trap: 3 : 5 is the reversed ratio — the alloy nearer the target is needed in larger quantity.
By alligation, X : Y = (2/3 − 5/8) : (5/8 − 3/5) = (1/24) : (1/40) = 40 : 24 = 5 : 3.
Check: 5 kg of X gives 3 kg copper, 3 kg of Y gives 2 kg copper; total 5 kg copper in 8 kg = 5/8. ✓
Trap: 3 : 5 is the reversed ratio — the alloy nearer the target is needed in larger quantity.
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