Question
Tap A can fill a tank in 8 hours and tap B can empty the tank in 12 hours. How long would it take to fill the empty tank if both of them are opened together?
- 12 hours
- 36 hours
- 48 hours
- 24 hours
Hint:
There are two taps A and B. Tap A fills the tank. Tap B empties the tank. We have to find the time required to fill the tank if both of them are working simultaneously. We will find level of tank filled in one hour for each of the tanks. Using this information, we will find the time to fill the tank completely.
The correct answer is: 24 hours
The time taken by tap A to fill the tank is 8 hours.
The level of tank filled in 1 hour by tap A is A = 
The time take by tap B to empty the tank is 12 hours.
The level of tank emptied in 1 hour by tap B is B =
They are working simultaneously.
We have to find the time required to fill the tank.
We can find the level filled when both are working simultaneously.
Level filled by them simultaneously is
So, the time taken by the tank to be filled when both are running simultaneously is 24 hours.
For such questions, we should see if the taps are filling or emptying the tank. We should also be careful about subtraction or addition of fractions. We should make the denominator equal or take L.C.M before subtracting or adding.
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