How many children should be increased to make the school work complete in exact time?

Question

8 teachers and 10 children do a school work in same days as 4 teachers and 16 children do. 1 teacher and 3 children start a school work to finish it in 40 days. After 18 days 9/20th part of the school work had been finished.
How many children should be increased to make the school work complete in exact time?

Answer 1

Work = speed x time
(8 Teacher + 10 Children)x time =(4 Teacher + 16 Children)x time
Here both times are same therefore they cancel out
We get a ratio of T/C = 3/2

Now
(1T + 3C)x18 = 9/20 work
Remaining work = 11/20 work
And
C = 1/ (9x20)
So
(1T + 3C + xC)*22 = 11/20
Substituting T=3C/2
(9C/2 + xC) x 22 = 11/20
Substituting C = 1/(9x20)
X=0
Therefore 0 children needed to keep the deadline.