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

Part filled by (A + B + C) in 1 min = 1/10
Part filled by A in 1 min = 1/30
Part filled by B in 1 min = 1/40

Part filled by (A + B) in 1 min
= 1/30 + 1/40
= (4 + 3)/120
= 7/120

Therefore, Part filled by C in 1 min
= 1/10 - 7/120
= (12 - 7)/120
= 5/120
= 1/24
Therefore, Tap C will fill the cistern in 24 min.