A and B take 30 days to finish a work, B and C take 24 days to finish that particular work, C and A take 20 days to finish the same work. All of them can finish the work in 10 days and If B and C leave the job, then how many days does A take to finish the same work?

Let the total work is 120 units.
(just a trick, you can assume any value instead of 120).

Let​​​​Let a, b and c be the works done by them per day.

As per the question,

a+b = 120/30 = 4 units/day.

Similarly b+c =120/24= 5

c+a = 120/20=6

Solving these 3 equations, we get a= 2.5, b = 1.5, c=3.5.

In 10 days, they'll do 10*(7.5) = 75.

Remaining work = 120–75= 45

A can do 2.5 units work per day.
Then A will do 45 units work in 45/2.5 = 18 days