Question

A Pump can fill a tank with water in \[2\] hours. Because of a leak, it took $2\dfrac{1}{3}$ hours to fill the tank. The leak can drain all the water of the tank in:
A) $5$ hours
B) $7$ Hours
C) $8$ Hours
D) $14$ hours

Answer 1

Hint: This question is related to the work done, time taken and rate of the work. Make use of the concept of proportionality between rate of the work, work done and time taken. Rate is inversely proportional with time taken and directly proportional with work done. To know how question is done, check the complete step- by- step solution given below:

Complete step-by-step answer:
First, we will calculate the work done,
We know that, Rate of work done is inversely proportional to time taken,
$\therefore R = \dfrac{1}{T}$
So, work done by pump in filling the tank in \[2\] hours.
${R_1} = \dfrac{1}{2}$
Now, we will calculate the work done by pump in filling the tank in $2\dfrac{1}{3}$ hours
${R_2} = \dfrac{1}{{2\dfrac{1}{3}}}$
We will calculate mixed fraction into improper fraction,
$R = \dfrac{1}{{\dfrac{7}{3}}}$
${R_2} = \dfrac{3}{7}$
Now, we want to know that how many hours it will take the tank to drain the water,
For this we will calculate the work done by leak in 1 hour,
Work done by leak in one hour is given by
$ = {R_1} - {R_2}$
$ = \dfrac{1}{2} - \dfrac{3}{7}$
On subtracting we will get,
We will take L.C.M and then subtract
$\dfrac{{1 \times 7}}{{2 \times 7}} - \dfrac{{3 \times 2}}{{7 \times 2}}$
$\dfrac{7}{{14}} - \dfrac{6}{{14}}$
$ = \dfrac{1}{{14}}$
We know that rate of work done is $\therefore R = \dfrac{1}{T}$
Therefore, it will take $14$ hours for the leak to drain the tank.

Option D is the correct answer.

Note: You must be very clear with the concept of the work done, time taken and the rate of work done as they are important in solving such questions. If you want to cut short the solution, then you can solve this question in short as the solution given below.
Work done by the leak in 1 hour
$ = \dfrac{1}{2} - \dfrac{3}{7}$
$ = \dfrac{1}{{14}}$
Leak will empty the tank in 14 hours