Water is pumped in and out of a tank using an inlet and outlet pipe

To calculate the time taken to complete the work, we need the individual rates of the inlet and outlet pipes.
On the other hand, if we know the quantum of work to be done, we will not be able to calculate the time required, since we do not know the rates of working of the pipes.

From statement I alone, we know that the inlet pipe takes 20 minutes to fill an empty tank and the outlet pipe takes 60 minutes to empty a full tank.
Let the capacity of the tank be 60 litres (which is the LCM of 20 and 60), which also represents the work to be done. This means,

Rate of inlet pipe = \(\frac{Work done}{Time taken}\) = \(\frac{60}{20}\) = 3 litres per hour

Rate of outlet pipe = \(\frac{Work done}{Time taken}\) = \(\frac{60}{60}\) = -1 litre per hour (negative because it's the outlet pipe)

Therefore, when both of them are opened simultaneously, combined rate = 2 litres per hour. Since we know the combined rate, we can calculate the time taken by them, when working together.
Statement I alone is sufficient. Answer options can be A or D. Options B, C and E can be eliminated.

From statement II alone, we only know the capacity of the tank. From what you saw above, it will not be hard to understand that knowing the capacity alone will not help you find the rates. Hence, it wont be possible to calculate the time taken by them working together.
Statement II is insufficient.

The correct answer option is A.

Hope this helps!

I guess I am not able to think straight because of the person sitting next to me who is continuously talking.
Here is my doubt:
Why is the size of the tank not relevant ?
So Yeah we assume the capacity to be 60 and get inlet pipe work as +3 and outlet as -1 Which gives us a result of 30 minutes. But what if the size of the tank is 600. We get 300 minutes which is 5 hours.
What am I missing?

To see what you missed, work through the full problem with your second example of a size 600 tank.

If the tank has a capacity of 600, then the inlet pipe fills it at a rate of 600 units / 20 minutes = 30 units per minute, and the outlet pipe empties it at a rate of 600 units / 60 minutes = 10 units per minute.

Therefore, the net change is +20 units per minute.

So, to fill the entire thing, it will take 600 units / (20 units per minute) = 30 minutes. That's the same as with a size 60 tank.

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Now, try it with yet another different size tank. What if the size of the tank is 300 instead of 600? The inlet pipe fills 300 units in 20 minutes, so that's 15 units per minute. The outlet pipe empties 300 units in 60 minutes, so that's 5 units per minute. In total, we're at +10 units per minute. Filling the whole thing will take 300 units / (10 units per minute) = 30 minutes. Same value.

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And, with a variable: If the size of the tank is T units, the inlet pipe fills it at T/20 units per minute, and the outlet pipe empties it at T/60 units per minute. The net increase is T/20 - T/60 = 3T/60 - T/60 = 2T/60 = T/30 units per minute.

To fill a tank of size T, at T/30 units per minute, takes T/(T/30) = 30 minutes, no matter what T is. The reason T doesn't matter is that it cancels out in this solution!

ccooley
Thank you for your detailed explanation.
I knew I am missing something. Thank you!

To fill up the tank with both pipes open simultaneously, you need to consider the net inflow rate. The inlet pipe fills 1/20 of the tank per minute, and the outlet pipe empties 1/60 of the tank per minute. So, the net inflow rate is 1/20 - 1/60 = 1/30 of the tank per minute.

To fill the entire 100-gallon tank, it will take 100 / (1/30) = 3000 minutes.