Twelve children take sixteen days to complete a work which can be completed by 8 adults in 12 days. After working for 3 days, sixteen adults left and six adults and four children joined them. How many days will they take to complete the remaining work ?
A) 3 days B) 2 days C) 6 days D) 12 days
Answers
Step-by-step explanation:
Answer: C) 6 days
Explanation:
From the given data,
12 children 16 days work,
One child’s one day work = 1/192.
8 adults 12 days work,
One adult’s one day’s work = 1/96.
Work done in 3 days = ((1/96) x 16 x 3) = 1/2
Remaining work = 1 – 1/2 = 1/2
(6 adults+ 4 children)’s 1 day’s work = 6/96 + 4/192 = 1/12
1/12 work is done by them in 1 day.
1/2 work is done by them in 12 x (1/2) = 6 days.
Answer :
8 adults can complete it in 12 days. So, 16 adults will take half time i.e. 6 days to finish the work. However, they left after working for 3 days, completing half of the work.
Now, 12 children' capacity for full work was 16 days. For half of the work, they should take 8 days. However, only 4 children (1/3) joined. So, their capacity is 24 days (12*8/4) to complete the work.
8 adults should take 6 days for half work, but only 6 adults (3/4) joined, so their capacity is 8 days (6*4/3) to complete the work.
Now, putting these 6 adults & 4 children together, work done in 1 day will be : 1/8 + 1/24 = 1/6
So, they will take 6 more days to complete the remaining work.