We need the time taken by hole x to completely empty the barrel and also the time taken by hole y to completely empty the barrel then we can form an equation of the form \(\frac{1}{x} +\frac{1}{y} = \frac{1}{z}\) where x is the time taken by hole x working alone to completely empty the barrel and y is the time taken by hole y working alone to completely empty the barrel. z is the total time taken when both work together.

(1): Coolant flows from the 40-liter tank through hole X at a rate of 2.5 liters per hour. Since we do not know the total capacity , we cannot ascertain the total time x will take to empty the barrel , or even if we did , there is no info of how long y would take to completely empty the barrel INSUFF.

(2): Coolant flows from hole Y twice as fast as from hole X, at a rate that will completely empty the barrel in 8 hours alone. This can we written as \(\frac{1}{8} + \frac{2}{8} =\frac{1}{z}\) Using this we can calculate the value of z. SUFF.

Ans-B
_________________

Hi why is the formula 1/x + 1/y = 1/z?

Is it because volume of liquid is inversely proportional to time taken?

Posted from my mobile device

No, the formula is basically addition of individual rates of flow of coolant from two holes to find the net rate of flow of coolant from the tank by assuming the capacity of the tank as 1 unit.

Rate=Work/Time
If the volume of the tank is 1 unit (Work in this case), then rate of flow of coolant from hole Y= 1/8
Similarly, rate of flow of coolant from hole X=1/4
So, Net Rate= 1/8+1/4=1/Net Time

I hope it's clear now. Feel free to ask any doubt.
_________________