Question

A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already $\dfrac{1}{2}$ full and both the taps are opened together, will the tank be filled or emptied? How long will it take before the tank is either filled completely or emptied completely, as the case may be?
A. 4 minutes
B. 5 minutes
C. 6 minutes
D. 8 minutes

Answer 1

Hint: We have to observe the time taken by each of them to find if the tank will be filled or emptied. We need to find the part filled and emptied in 1 minute and subtract them to find the total part filled or emptied. Using the information, we have to find the time taken to fill or empty $\dfrac{1}{2}$ filled tank.

Complete Step-by-Step solution:
As the time taken to empty is less than the time taken to fill the tank , the tank will be emptied .
Hence we have to find the time taken to empty the $\dfrac{1}{2}$ filled tank.
If the tap can fill the tank in 16 minutes then part filled in 1 minute by the tap if run alone = $\dfrac{1}{{16}}$
If the tap can empty the tank in 8 minutes then part emptied in 1 minute by the tap if run alone =$\dfrac{1}{8}$
Part emptied in the tank when both taps are opened in 1 minute = $\dfrac{1}{8} - \dfrac{1}{{16}} = \dfrac{1}{{16}}$
Therefore time taken to empty ( 1 whole part ) complete tank will be 16 minutes if both are run together.
Hence the time taken to empty $\dfrac{1}{2}$ filled tank = $\dfrac{{16}}{2} = 8$ minutes

Note: Remember that in this particular type of question we need to think and observe the question properly. We need to divide the tank into parts and then solve the question according to the given information. Always remember that if the time taken is less than the work done would be more .