Multiple choice

The amount of work that five boys and one man can complete in a day, and the work that two women and two men can complete in a day, are 50% and 66⅔%, respectively of the total work that three women, four boys and two men can complete in a day. Two women, three boys and two men can complete what percentage of the work in a day?

  1. 80%

  2. 83.33%

  3. 87.5%

  4. 78%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let W, B, M be daily work of woman, boy, man. 5B + M = 0.5(3W + 4B + 2M) => 10B + 2M = 3W + 4B + 2M => 3W = 6B => W = 2B. 2W + 2M = (2/3)(3W + 4B + 2M) => 6W + 6M = 6W + 8B + 4M => 2M = 8B => M = 4B. Target: 2W + 3B + 2M = 2(2B) + 3B + 2(4B) = 4B + 3B + 8B = 15B. Total work = 3W + 4B + 2M = 3(2B) + 4B + 2(4B) = 6B + 4B + 8B = 18B. Percentage = 15/18 = 5/6 = 83.33%.

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