Multiple choice

8 men can finish a piece of work in 21 days. 14 men started working and after 3 days they were replaced by 9 women. These 9 women finished the remaining work in 24 days. In how many days can 9 women finish the whole work?

  1. 32

  2. 31

  3. 30

  4. 29

  5. 28
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total work = 8 * 21 = 168 man-days. 14 men work for 3 days = 42 man-days. Remaining work = 168 - 42 = 126 man-days. 9 women do this in 24 days, so 9 women's efficiency = 126/24 = 5.25 man-days per day. Total work for 9 women = 168 / 5.25 = 32 days.

AI explanation

The total work is 8 men multiplied by 21 days, or 168 man days. 14 men working for 3 days complete 42 man days, leaving 126 man days of work. The 9 women complete this remaining 126 man days of work in 24 days, so dividing 126 by 24 shows 9 women do 5.25 man days of work per day. To find how long it takes them to do the entire 168 man days, divide 168 by 5.25 to get exactly 32 days.

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