Multiple choice

If I have to appoint 12 men and 16 boys for 6 days to do a job and 16 men and 30 boys can do it in 4 days, then find the ratio of work capacity of men and boys?

  1. 1: 2

  2. 3: 1

  3. 1: 4

  4. 5: 1

  5. 2: 1
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B Correct answer
Explanation

Let work capacity of 1 man = M and 1 boy = B per day. From first condition: 12M + 16B = 1/6 (work per day). From second: 16M + 30B = 1/4. Solving these simultaneous equations: Multiply first by 12 and second by 6 to get 144M + 192B = 2 and 96M + 180B = 1.5. Subtracting gives 48M + 12B = 0.5, so 4M + B = 1/24, which means B = 1/24 - 4M. Substituting back gives M:B = 3:1.

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