Multiple choice

If 3 men and 4 boys can do a piece of work in 6 days and 6 men and 3 boys can do it in 4 days. Compare the efficiency of a man to that of a boy.

  1. 1:1

  2. 2:1

  3. 1:2

  4. 3:1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let efficiency of 1 man = m work/day, 1 boy = b work/day. Then 3m + 4b = 1/6 and 6m + 3b = 1/4. Solving these equations: from the first, 6m + 8b = 1/3. Subtracting the second: 5b = 1/3 - 1/4 = 1/12, so b = 1/60. Substituting: 6m = 1/4 - 3/60 = 1/4 - 1/20 = 4/20 = 1/5, so m = 1/30. The ratio m:b = (1/30):(1/60) = 2:1.

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