Question

Nidhi can do a piece of work in 20 days and Seema in 30 days they began to work together but Nidhi left after some days. Seema finished the remaining work in 10 days. After how many days did Nidhi leave?

Answer 1

Nidhi does the work in 20 days.
in 1 day, Nidhi does = (1/20) of the work
Seema does the work in 30 days.
in 1 day, Seema does = (1/30) of the work

Seema finished rest work in 10 days,
in 10 days, she did = (1/30)*10 = 1/3 of the work
So together they did = 1-(1/3) = 2/3 of the work.

In 1 day, both can do = 1/20 + 1/30 = (3+2)/60 = 5/60 = 1/12 of the work
so 1/12 of the work is done in 1 day

2/3 of the work can be done = $\frac{2/3}{1/12} = \frac{2}{3}*12=8\ days$ 
So Nidhi left after 8 days.