Question

30men can do a work in 10days.But only a man started the work and every day a new person started joining the work.In how many days the work will be completed?

Answer 1

300 men can do a work in 1 day
1 men can do 1/300 work in 1 day
in the first day work done = 1/300
in second day work done = 1/300 + 2/300 = (1+2)/300
similarly in n th day work done is 1 complete
therefore (1+2+3+4+.....+n)/300 = 1
1+2+3+4+....+n = 300
$\frac{n}{2} (2a + (n - 1)d)$
where a =1 , d = 1
by solving this we get n = 24
hence answer is the work will completed in 24 days