A, B and C can alone do a task in 40, 120 and 36 days respectively. A and B together work for 20 days and leave the task incomplete. C resumes it and completes it alone. How many days did C take to complete it?

A, B and C can alone do a task in 40, 120 and 36 days respectively.

The LCM of 40, 120 and 36 is 360 which is the total work.

The efficiency of A = $$\frac{360}{40}$$ = 9 units/day

The efficiency of B = $$\frac{360}{120}$$ = 3 units/day

The efficiency of C = $$\frac{360}{36}$$ = 10 units/day

 A and B together work for 20 days and leave the task incomplete. C resumes it and completes it alone.

Let's assume the number of days C work is 'y'.

$$9\times20 + 3\times20 + 10\times y = 360$$

180 + 60 + 10y = 360

240 + 10y = 360

10y = 360-240 = 120

y = 12

The number of days taken by C to complete the remaining work = y = 12