Question

A tap can fill a tank of 500 litres in 3 hours 30 minutes. In how much time will it fill one fifth of the tank?

Answer 1

Hint:In the above given question, make the use of the unitary method. First of all, calculate the volume of the tank which is to be filled, then, find the time taken for filling 1 litre and then subsequently the time for the required volume can be calculated.

Complete step-by-step answer:
We are given the question that a tap fills a tank of 500 litres in 3 hours and 30 minutes.
So, the one fifth of 500 litres tank contains $\dfrac{1}{5} \times 500$=100 litres
We know that the time taken to fill 500 litres = 3.5 hours
Therefore, by using a unitary method, we can obtain the time taken by the tap to fill 100 litres.
A tank of 500 litres is filled in = 3.5 hours.
A tank of 1 litre will be filled in = $\dfrac{{3.5}}{{500}}$hours.
So, a tank of 100 litres will be filled in = $\dfrac{{3.5}}{{500}} \times 100$hours.
$ = \dfrac{{35}}{{500 \times 10}} \times 100$hours
$ = \dfrac{{35}}{{50}}$ hours
= 0.7 hours
Now, we know that 1 hour = 60 minutes.
Therefore, we get
$ = 0.7 \times 60$minutes
= 42 minutes
 Hence, a tap can fill one fifth of the tank in 42 minutes.

Note: In these types of questions, make the conversion changes carefully like hours can be converted into minutes by multiplying with 60, whereas the minutes can be converted into hours by dividing by 60 and so on. Calculating the time required for 1 litre of the water to be filled is a very important step in the solution.