Twenty-four men can complete a work in sixteen days. Thirty-two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working and worked for twelve days. How many more men are to be added to complete the remaining work in 2 days?
Explanation
We are given:
24 men complete the work in 16 days → 1 man's 1-day work = 1/24×16=1/38432 women complete the work in 24 days → 1 woman's 1-day work = 1/32×24=1/768
16 men and 16 women work for 12 days
Step 1: Work done by 16 men and 16 women in 12 days
Work done by 16 men in 1 day = 16×1/384=16/384=1/24
Work done by 16 women in 1 day = 16×1/768=16/768=1/48
Total work done in 1 day = 1/24+1/48=2/48+1/48=3/48=1/16
Total work done in 12 days = 12×1/16=12/16=¾
Step 2: Work remaining
Total work = 1
Work done = ¾
Work remaining = 1−3/4=1/4
Step 3: Additional men required
The remaining work must be completed in 2 days.
Let x be the number of additional men needed.
Work done by (16 + x) men in 1 day = (16+x)×1384(16 + x)
Work done in 2 days = 2×(16+x)×1384=142
Solving for x:
(16+x)×2/384=¼
16+x=1/4×384/2=384/8=48
x=48−16=32
The closest option is 36 men
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