A tap can empty a tank in one hour. A second tap can empty it in 30 minutes. If both the taps operate simultaneously, how much time is needed to empty the tank?
A tap can empty a tank in one hour. A second tap can empty it in 30 minutes. If both the taps operate simultaneously, how much time is needed to empty the tank?
[A]45 minutes
[B]20 minutes
[C]40 minutes
[D]30 minutes
20 minutes
1 hour = 60 minutes
Rate of emptying the tank by the two taps are $latex \frac{1}{60}&s=1$ and $latex \frac{1}{30}&s=1$ of the tank per minute respectively.
Rate of emptying the tank when both operate simultaneously =
$latex = \frac{1}{60} + \frac{1}{30} = \frac{1+2}{60} = \frac{3}{60} = \frac{1}{20}&s=1$
of the tank per minute.
∴ Time taken by the two taps together to empty the tank = 20 minutes.
Hence option [B] is the right answer.