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A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 24 hours. How many liters does the cistern hold?
  • a)
    4010 litre
  • b)
    2220 litre
  • c)
    1920 litre
  • d)
    2020 litre
Correct answer is option 'C'. Can you explain this answer?
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Let's solve this problem step by step:

Let's assume the capacity of the tank is 'C' liters.
We are given that the leak in the bottom of the tank can empty the full tank in 6 hours. This means that in 1 hour, the leak can empty 1/6th of the tank. Therefore, the leak rate is C/6 liters per hour.

We are also given that an inlet pipe fills water at the rate of 4 liters per minute. Since there are 60 minutes in an hour, the inlet pipe fills water at the rate of 4*60 = 240 liters per hour.

When the tank is full and both the inlet pipe and the leak are open, the net outflow rate is the difference between the filling rate and the leak rate. Therefore, the net outflow rate is 240 - C/6 liters per hour.

We are given that when the tank is full, it takes 24 hours for the tank to empty. Therefore, the total outflow during this time is (240 - C/6) * 24.

Since the tank is full at the beginning, the total inflow should be equal to the total outflow. Therefore, (240 - C/6) * 24 = C.

Now, let's solve this equation to find the value of C:

(240 - C/6) * 24 = C
5760 - 24C/6 = C
5760 - 4C = C
5C = 5760
C = 5760/5
C = 1152

Therefore, the cistern holds 1152 liters.

However, none of the provided options match this answer. Therefore, there might be an error in the question or the options.
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