Question

A,B,C together can finish a price of work in 4 days;A alone can do it in 12 days and B can do in 18 days,then find the time taken by C alone to finish the work

Answer 1

In 4 days, A & B together do 4*(1/12 + 1/18) = 5/9 of the work . 

So, in 4 days C does (1 - 5/9) = 4/9 of the work .

So, C does 1/9 of work in 1 day.

Hence, C alone completes the work in 9 days .

Answer 2

Total time taken by A , B and C to finish the work = 4 days

Work done by them together in one day = 1/4

Now, 
TIme taken by A to complete the work = 12 days

Work done by A in one day = 1/ 12.

Time taken by B to complete the whole work = 18 days

Work done by B in one day = 1 /18

Now,
Let the time taken by C be x days

So, the work done by C alone in one day = 1 /x.

Now,

work done in one day by all the three together
= Sum of the work done by all the three A , B and C in one day

1 / 4 = 1 / 12 + 1/18 + 1/ x

1/4  = 3/36 + 2/36 + 1/x

1/x = 1/4 - 5/36

1/x = 9/36 - 5/36

1/x = 4/36

1/x = 1/9
x = 9 days

Therefore, C alone finishes the same work in 9 days.

Hope this helps you !!!