Two taps can fill a tank in 30 minutes and 40 minutes. Another tap can empty it in 24 minutes. If the tank is empty and all the three taps are kept open, in how much time the tank will be filled?

60 minutes.

Step-by-step explanation:

Find the time for filling the tank with the first 2 taps:

1/30 + 1/40 = 1/x

Multiply through by the LCD 120x:

4x + 3x = 120

x = 120 / 7

= 17.14 minutes.

When the other tap is emptying the tank we have

1/17.14 - 1 / 24 = 1 / x

0.05834 -.04167

= 0.01667

so x = 1 / 0.01667

= 60 minutes to the nearest minute.