Question

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?

Answer 1

Hint: To solve this question, first of all we need to find the rate of emptying the tank with respect to each of the taps. After finding, first we need to convert the time from hours to minutes and then we need to add the rate of both the tape in order to find the rate of emptying of the tank, when both the taps are opened together. After the rate, we can easily find the time taken to empty the tank when both the taps are together opened.

Complete step by step answer:
As given in the question,
Time taken by tap A to empty the tank \[=1\text{ hour}=60\text{ minutes}\]
Time taken by tap B to empty the same tank \[=30\text{ minutes}\]
The time which we need to find out is when both the taps are opened together.
Rate of emptying of tank by tap A per minute \[=\dfrac{1}{60}\]
Similarly, the rate of emptying of tank by tap B per minute \[=\dfrac{1}{30}\]
Now, the rate of emptying of tank by both the taps together,
\[\begin{align}
  & =\dfrac{1}{60}+\dfrac{1}{30} \\
 & =\dfrac{1+2}{60} \\
 & =\dfrac{3}{60} \\
 & =\dfrac{1}{20} \\
\end{align}\]

Hence, we can say that, the time taken to empty the tank by both the taps together is 20 minutes.

Note: To solve this question, some students try to solve this directly without finding the rate, which will make the solution wrong. Some students try to multiply the rates of both the taps instead of adding, to find the final rate which will also make the solution wrong.