Single correct option
Alloy P contains copper and zinc in the ratio 3 : 2, and alloy Q contains them in the ratio 5 : 3. In what ratio should P and Q be mixed (by weight) to obtain an alloy with copper and zinc in the ratio 8 : 5?
- A. 5 : 8
- B. 8 : 5
- C. 3 : 5
- D. 5 : 3
Show answer and solution
Answer: (A) 5 : 8
Work with the fraction of copper: P = 3/5 = 0.6, Q = 5/8 = 0.625, target = 8/13 ≈ 0.6154.
By alligation, P : Q = (Q − target) : (target − P) = (5/8 − 8/13) : (8/13 − 3/5) = (1/104) : (1/65) = 65 : 104 = 5 : 8.
Sanity check: the target (0.6154) lies closer to Q (0.625) than to P (0.6), so more of Q is needed — consistent with 5 : 8, not 8 : 5.
Tip: Always alligate the fraction of ONE component in each alloy, never the ratios themselves.
By alligation, P : Q = (Q − target) : (target − P) = (5/8 − 8/13) : (8/13 − 3/5) = (1/104) : (1/65) = 65 : 104 = 5 : 8.
Sanity check: the target (0.6154) lies closer to Q (0.625) than to P (0.6), so more of Q is needed — consistent with 5 : 8, not 8 : 5.
Tip: Always alligate the fraction of ONE component in each alloy, never the ratios themselves.
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