Three taps A, B and C together can fill an empty cistern in 10 minutes. The tap A alone can fill it in 30 minutes and the tap B alone in 40 minutes. How long will the tap C alone take to fill it?

A, B and C together can fill 100% empty tank in 10 minutes
Work rate of (A + B + C) = $$\frac{{100}}{{10}}$$ = 10% per minute
A alone can fill the tank in 30 minutes
Work rate of A = $$\frac{{100}}{{30}}$$ = 3.33% per minute
B alone can fill the tank in 40 minutes
Work rate of B = $$\frac{{100}}{{40}}$$ = 2.5%
Work rate of (A + B) = 3.33 + 2.5 = 5.83% per minute
Work rate of C,
= Work rate of (A + B + C) - (A + B)
= 10 - 5.83 = 4.17% per minute
So, C takes = $$\frac{{100}}{{4.17}}$$ ≈ 24 minutes to fill the tank