Question

3 Pumps who work 8 hours per day empty the tank in 2 days. How many hours per day will 4 pumps use to empty the tank in 1 day?

Answer 1

Hint: It is given that $3$ Pumps who work $8$ hours per day empty the tank in $2$ days. From this, we need to find the word done by three pumps in one hour and also we need to calculate the work done by one pump in one hour. Therefore, we shall get the required work done by four pumps in an hour. That is our question too.

Complete step-by-step solution:
It is given that $3$ Pumps who work $8$ hours per day empty the tank in $2$ days.
$3$ Pumps work $8$ hours per day. That is, $3$ Pumps work $8 \times 2$ hours in $2$ days.
That is, $3$ Pumps work $16$ hours to empty the tank in $2$ days.
From this, we need to calculate the word done by three pumps in one hour.
We have calculated that $3$ Pumps work $16$ hours to empty the tank,
Hence, the work done by $3$ pumps in $1$ hour $ = \dfrac{1}{{16}}$ . It refers to three pumps that take $16$ hours to empty the tank in a day.
And also we need to calculate the work done by one pump in one hour.
Therefore, the work done by $1$ pumps in $1$ hour$ = \dfrac{1}{{3 \times 16}}$ .
                                                                                     $ = \dfrac{1}{{48}}$
It refers that one pump takes $48$ hours to empty the tank in a day.
Now, we shall get the required work done by four pumps in an hour.
The work done by $4$ pumps in$1$ hour $ = \dfrac{1}{{48}} \times 4$
                                                                        $ = \dfrac{1}{{12}}$
Hence, the work done by $4$ pumps in $1$hour$ = \dfrac{1}{{12}}$.
It refers that four pumps take $12$ hours to empty the tank in a day which is the required answer.

Note: We may confuse that $\dfrac{1}{{12}}$ is the required answer but it is just the work done by the four pumps and our question is to calculate how many hours the four pumps will take to empty the tank in a day. Here, $\dfrac{1}{{12}}$ refers to four pumps taking $12$ hours to empty the tank in a day which is the required answer.