Multiple choice

2 men or 3 women or 5 boys can complete a job in 18 days. In how many days can 8 men, 9 women and 10 boys complete the same job working together?

  1. 2

  2. 4

  3. 6

  4. 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

2 men = 3 women = 5 boys = 1 unit of work per 18 days. This means 1 man = 9 units/day, 1 woman = 6 units/day, 1 boy = 3.6 units/day. Total work = 2 * 9 * 18 = 324. Working together, 8 men + 9 women + 10 boys = 72 + 54 + 36 = 162 units/day. Days = 324 / 162 = 2.

AI explanation

If 2 men or 3 women or 5 boys complete the job in 18 days, their daily work is 1/18. Therefore, 2 men equal 1/18 daily work, meaning 1 man equals 1/36. Also, 3 women equals 1/18, meaning 1 woman equals 1/54. Furthermore, 5 boys equals 1/18, meaning 1 boy equals 1/90. For 8 men, 9 women, and 10 boys, the daily work sums to 8/36 + 9/54 + 10/90. Finding a common denominator of 180, this becomes 40/180 + 30/180 + 20/180 = 90/180 = 1/2. Therefore, they complete the work in 2 days.

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