An outlet pipe empties a tank in 5 hours

If we consider that both pipes are opened when tank get filled in 10 hours, the capacity of the tank will be 100 liters

In 10 hours, the outlet pipe must have done work of emptying a full tank(say capacity is c).
But what happened is, in 10 hours, we have a full tank. Thus the inlet pipe must have, in ten hours, done the work of filling the tank twice(or in other words, work equal to 2c).

Thus the capacity of the tank is half of what the inlet pipe can do in 10 hours.

\(\frac{1}{2} * 10 * \frac{1}{3} * 60\)

Answer 100(C)

outlet= 50% in 5 h so, 100% in 10 hr
capacity=10x
inlet=1/3 lit per min=1/3*60=20 lit per hr
atq
20*10 - 10x=10x
x=10
capacity= 10*10=100
ans: B

Hi All,

We're told that an outlet pipe empties a tank in 5 hours when the tank is 50% full and that an inlet pipe lets water in at 1/3 liters per min. We're told that the tank starts off empty and took 10 hours to fill the tank. We're asked for the capacity of the tank.

Although the prompt does not state it, we're meant to assume that both pipes are 'working' at the same time. This question gives us two rates, but provides the information in different units. Thus, we have to 'modify' the given information a bit:

Inlet Pipe = 1/3 liters/min = (60 mins)(1/3 liter/min) = 20 liters/hour
Outlet Pipe = 5 hours to remove HALF the tank = (1/2 tank)/5 hours = 1/10 of the tank is emptied per hour

Since it take 10 hours to fill the tank, we have...
(20 liters)(10 hours) = 200 liters going IN
(1/10 tank)(10 hours) = 1 "full tank" going OUT

In algebraic terms, that would be: 200 - X = X
X = 100 liters

Final Answer:

GMAT assassins aren't born, they're made,
Rich

The answer provided is incorrect unless specified that both the inlet and outlet pipe are working together.

We can let c = the full capacity of the tank, in liters. If the outlet pipe empties the tank in 5 hours when the tank is 50% full, then it will empty the tank in 10 hours when the tank is 100% full. Therefore, the rate of the outlet pipe c/10 liters per hour.

Since the inlet pipe has a rate of 1/3 liters per minute, its rate is 1/3 x 60 = 20 liters per hour. Since it took 10 hours to fill the tank completely (while the outlet pipe is open), we can create the equation:

10(20 - c/10) = c

200 - c = c

200 = 2c

100 = c

Answer: B