Multiple choice

16 men and 12 women can complete a work in 20 days. 18 women can complete the same work in 40 days. In how many days will 12 men and 27 women complete the same work?

  1. 12

  2. 16

  3. 18

  4. 24
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

16M+12W=1/20 work/day. 18W=1/40 work/day => 1W=1/720. 16M+12(1/720)=1/20 => 16M=1/20-1/60=2/60=1/30 => 1M=1/480. 12M+27W = 12/480 + 27/720 = 1/40 + 3/80 = 5/80 = 1/16. Time = 16 days.

AI explanation

Using the LCM method, let the total work be 360 units. From the second condition, 18 women complete the work in 40 days, meaning one woman does 360 divided by 18 divided by 40, which equals 0.5 units per day. From the first condition, 16 men and 12 women complete 360 units in 20 days, giving a daily output of 18 units; since the 12 women contribute 6 units, the 16 men contribute 12 units, making one man equal to 0.75 units per day. For 12 men and 27 women, the daily output is 12 times 0.75 plus 27 times 0.5, equaling 9 plus 13.5, which is 22.5 units per day. The time required is 360 divided by 22.5, which equals 16 days.

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