Sixteen men can complete a work in twelve days. Twenty-four children can complete the same work in eighteen days. Twelve men and eight children started working and after eight days three more children joined them. How many days will they now take to complete the remaining work?
Answer: 4 days
Explanation
Step 1: Work Done by One Man and One Child in One Day
16 men complete the work in 12 days.
Work done by 16 men in 1 day = 1/12
Work done by 1 man in 1 day = 1/12×16=1/192
24 children complete the work in 18 days.
Work done by 24 children in 1 day = 1/18
Work done by 1 child in 1 day = 1/18×24=1432
Step 2: Work Done by 12 Men and 8 Children in One Day
Work done by 12 men in 1 day = 12×1/192=12/192=1/16
Work done by 8 children in 1 day = 8×1/432=8/432=1/54
Total work done per day by 12 men and 8 children = 1/16+1/54
Taking LCM (16, 54) = 432,
27/432+8/432=35/432
So, work done per day = 35/432
Step 3: Work Done in 8 Days
Work done in 8 days = 8×35/432=280/432
Remaining work = 1−280/432=152/432
Step 4: Work Done After Adding 3 More Children
Work done by 3 children in 1 day = 3×1/432=3/432
New work rate per day = 35/432+3/432=38/432
Remaining days required = 152/432/38/432=4 days
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