Correct option is A
Given:
18 men can complete the work in 64 days.
9 women can complete the work in 108 days.
7 children can complete the work in 216 days.
Concept Used:
Work done is inversely proportional to the number of days taken.
Formula Used:
Work Rate of one person=Number of days taken to complete the work by that person1
Solution:
18 men can complete the work in 64 days, so the work rate of 1 man is:
Rate of one man=18×641=11521 (work per day)
9 women can complete the work in 108 days, so the work rate of 1 woman is:
Rate of one woman=9×1081=9721 (work per day)
7 children can complete the work in 216 days, so the work rate of 1 child is:
Rate of one child=7×2161=15121 (work per day)
Work rate of 16 men:
16×11521=115216=721 (work per day)
Work rate of 9 women:
9×9721=9729=1081 (work per day)
Work rate of 21 children:
21×15121=151221=721 (work per day)
Now,
Total work rate=721+1081+721 =721+1081+721 =2163+2162+2163=2168=271
Since the total work rate is
271 work per day, the time to complete the work is:
Time=2711=27 days
Thus, 16 men, 9 women, and 21 children together will take 27 days to complete the work.
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