Q) 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

a) 3 days              b) 5 days               c) 7 days                     d) None of these

Ans:

Let w be the work done by a woman in 1 day and c be the work done by a child in 1 day

Hence, by given 1st condition: 10 w = 1/7

∴ w = 1/70

and by given 2nd condition: 10 c= 1/14

∴ c = 1/140

∴ Now, work done by 5 women and 10 children = 5w + 10 c = 5 (1/70) + 10 (1/140)

= 5/70 + 1/14 = 5/70 + 5/70 =10/70 = 1/7

Since time taken by 5 women and 10 children together to finish 1/7 work = 1 day

∴ time taken by 5 women and 10 children together can finish full work = 1/(1/7) = 7 days

Alternate method:

Time taken by 10 women to complete a work = 7 days  (given)

∴ Time taken by 5 women to complete a work = 14 days (time increases if labour decreases)

Time taken by 10 children to complete a work = 14 days  (given)

Now if 5 women and 10 children are deployed, they will do 2 times full work in 14 days

∴ Time taken by 5 women & 10 children to complete one full work = 14/2 = 7 days