Painter A can paint a house in 40 days and Painter B can do it in 60 days. With the help of C, they did the job in 20 days only. Then, C alone can do the job in:

Let the total work be the LCM of 40,60, and 20, which is 120 units.
Efficiency of A =
40
120
​
=3 units/day

Efficiency of B =
60
120
​
=2 units/day

Combined efficiency of A, B, and C working together =
20
120
​
=6 units/day

We can find the individual efficiency of C by subtracting the efficiencies of A and B from their combined efficiency:

Efficiency of C=(Efficiency of A+B+C)−(Efficiency of A+Efficiency of B)
Efficiency of C=6−(3+2)=6−5=1 unit/day
The time taken by C alone to complete the total work is:

Time taken by C=
Efficiency of C
Total Work
​
=
1
120
​
=120 days