Question

A tap can fill a tank in 15 minutes, another tap can empty it in 20 minutes. Initially the tank is empty. If both the taps start functioning then time taken to fill the tank is
A.1 hour
B.1 hour 40 minutes
C.90 minutes
D.2 hours

Answer 1

Hint: Find part of tank filled by each tap in a minute. Then add them which tells part of the tank filled when both the tap is opened in a minute. Hence, find what is asked.

Complete step by step answer:
In the question we can see that one tap can fill a tank in 15 minutes and another tap cam empty in 20 minutes. We have to find the time at which tank will be filled up if initially that tank was empty.
We know that the 1st tap can fill a tank in 15 minutes.
So, in other words we can say that in 1minute 1st tap can fill $\dfrac{1}{15}$ part of the tank.
Now, we know that the 2nd tap can empty a tank in 20 minutes.
We can also write the same statement as that 2nd tap can fill a tank in $-20$ minutes.
So, in other words we can say that in 1minute 2nd tap can fill $\dfrac{1}{-20}$ part of the tank.
So, in the question we are told that both the taps are opened together at the same time.
The part of the tank filled when both the taps are opened in 1minute is $\left( \dfrac{1}{15} \right)+\left( \dfrac{1}{-20} \right)$ .
So, on calculation by taking L.C.M we get,
$\dfrac{20-15}{300}=\dfrac{5}{300}=\dfrac{1}{60}$
So, $\dfrac{1}{60}$ part of the tank is filled in 1minute if both the taps are opened.
Hence, the whole part or full tank can be filled in 60 minutes.
We know that 1hour contains 60minutes.
So, the whole tank is filled up in 1 hour.

Correct option is ‘A’.

Note: The same process can be applied for 3 or more taps contained or asked in the question. All can be functioned and calculated at one go.