**Concept: The question tests on the area of rates**

**Solution:**

LCM of 10, 15, and 20 = 60

Assume we need to do 60 units of work

A + B in 1 day does 60/10 = 6 units

B + C in 1 day does 60/15 = 4 units

C + A in 1 day does 60/20 = 3 units

Adding 2 * (A + B + C) = 13 units (Work done in 2 days when all 3 work together)

A + B + C = 13/2

C alone = (A + B + C) - (A + B) = 13/2 - 6 = 1/2 unit per day

In 2 days A, B and C finish 13 units after which A leaves

B and C in 2 days finish 2 * 4 = 8 units

Total work done = 21 units and work remaining = 60 - 21 = 39 units

C does 1/2 unit per day, so to do 39 units c will take 78 days

Option D