Final answer:
The capacity of the tank is found by calculating the rate at which the leak empties the tank and accounting for the additional water from the tap. The equation 1/8 tank per hour equals 1/12 tank per hour plus 6 liters per hour is solved to find that the tank's capacity is 144 liters. The Correct Answer is Option. C.
Step-by-step explanation:
The question is asking us to find the capacity of the tank given that there is a leak that can empty it in 8 hours and that a tap which admits 6 liters per hour is opened when the tank is full, resulting in the tank being emptied in 12 hours.
First, we can establish the rate at which the tank is being emptied without the tap as 1/8 tank per hour since it empties in 8 hours. With the tap open, it empties in 12 hours, which is a rate of 1/12 tank per hour.
However, this slower rate includes the addition of 6 liters per hour. Thus, the effect of the leak alone when the tap is open is (1/12 tank/hour) + (6 liters/hour).
To find the capacity, we set the rates equal since they both represent the leak's capacity to empty the tank:
(1/8 tank/hour) = (1/12 tank/hour) + (6 liters/hour).
Solving this equation will give us the capacity of the tank in liters.
After solving:
1/8 - 1/12 = 6 liters/hour
3/24 - 2/24 = 6 liters/hour
1/24 tank = 6 liters
Tank capacity = 24 * 6 = 144 liters.
The capacity of the tank is therefore 144 liters, which corresponds to option C in the question.