Single correct option
Vessel A contains milk and water in the ratio 5 : 3 and vessel B contains milk and water in the ratio 2 : 3. In what ratio should the contents of A and B be mixed so that the resulting mixture has equal quantities of milk and water?
- A. 5 : 4
- B. 4 : 5
- C. 3 : 4
- D. 2 : 3
Show answer and solution
Answer: (B) 4 : 5
Work with the fraction of milk. In A it is 5/8 = 0.625, in B it is 2/5 = 0.4, and the target is 1/2 = 0.5.
By alligation, A : B = (target − B) : (A − target) = (0.5 − 0.4) : (0.625 − 0.5) = 0.1 : 0.125 = 4 : 5.
Check: 4 litres of A give 2.5 L milk, 5 litres of B give 2 L milk; total milk 4.5 out of 9 L = 1/2. ✓
The distractor 5 : 4 comes from placing the differences the wrong way round — the vessel whose concentration is farther from the target gets the smaller share.
By alligation, A : B = (target − B) : (A − target) = (0.5 − 0.4) : (0.625 − 0.5) = 0.1 : 0.125 = 4 : 5.
Check: 4 litres of A give 2.5 L milk, 5 litres of B give 2 L milk; total milk 4.5 out of 9 L = 1/2. ✓
The distractor 5 : 4 comes from placing the differences the wrong way round — the vessel whose concentration is farther from the target gets the smaller share.
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