Question

Two pipes can fill a tank in  $ 20$ minutes and  $ 30$ minutes respectively. If both the pipes are opened simultaneously, then the tank will be filled in:

A) 10 minutes

B) 12 minutes

C) 15 minutes

D) 25 minutes

Answer 1

Hint: In this type of time work problems. We will find a solution to a given problem by a unitary method. In this we first calculate work done by first pipe in one minute and then work done by second pipe in one minute and then finding total work done by both pipes in one minute and taking reciprocal of it will give total time taken by both pipes to fill a tank. 

Complete step-by-step answer:

Given that two pipes can fill a tank in  $ 20\;minutes $ and  $ 30\;minutes $ respectively.

Let's name two pipes as A and B.

Therefore, we can say that pipe A can fill a tank in $ 20\;minutes $ .

And pipe B can fill a tank in $ 30\;minutes $ .

For this type of problem we use a unitary method. 

In this we first calculate the work done by each pipe in a minute and then find work done by both pipes in one minutes by adding their one minutes work. 

Work done by pipe A in  $ 1\;minute $ is = $ \dfrac{1}{{20}} $ 

Work done by pipe B in  $ 1\; minute$ is =  $ \dfrac{1}{{30}} $ 

Therefore, work done by both pipes A and B in  $ 1 $ minute is =  $ \dfrac{1}{{20}} + \dfrac{1}{{30}} $ 

Simplifying, above by taking LCM. We have,

Work done by both pipes A and B in  $ 1 $ minute $  = \dfrac{{3 + 2}}{{60}} $ 

$  \Rightarrow  $ Work done by both pipes A and B in  $ 1 $ minute $  = \dfrac{5}{{60}} $ 

$  \Rightarrow  $ Work done by both pipes A and B in  $ 1 $ minute $  = \dfrac{1}{{12}} $ 

Therefore, time taken by both pipes when open together will be given as reciprocal of work done by both pipes in one minute. 

Hence, time taken to fill the tank by both pipes will be =  $ 12\;minutes. $ .

So, the correct answer is “Option B”.

Note: In this type of problem in which time taken to fill tank by both pipes are given and to find time when both pipes work together students might add directly time taken by both pipe individual but this will be wrong way to calculate as on doing so value of time will be greater as of their individual time but generally it would be less as now work is done by two pipes. Hence, for the correct answer we use the unitary method and using it we will find the correct solution to the given problem.