4101. 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?
- A. 9 days
- B. 5 days
- C. 4 days
- D. 10 days
Check answer and explanation
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 = 1 52/432/38/432=4 days