Multiple choice

If 2 men and 3 boys can do a piece of work in 10 days and 3 men and 2 boys can do it 8 days, how long will 2 men and 1 boy take to do it

  1. 15

  2. 18

  3. 12.5

  4. 16
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let M be the work of a man and B be the work of a boy per day. 10(2M + 3B) = 1, so 20M + 30B = 1. 8(3M + 2B) = 1, so 24M + 16B = 1. Solving the system: 80M + 120B = 4 and 180M + 120B = 7.5. Subtracting gives 100M = 3.5, M = 0.035. Then 30B = 1 - 20(0.035) = 0.3, B = 0.01. 2M + 1B = 2(0.035) + 0.01 = 0.08. Time = 1 / 0.08 = 12.5 days.

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