There is a leak in the bottom of tank which can empty the tank in 8hours if a tap is open to the tank time taken to empty the tank is 12 hours if tap admitted 6liter water perhour find the capacity of tank
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the addition of water increases the emptying time by 50%
... so it must increase the apparent volume of the tank by 50%
the added water is 50% (half) of the tank volume
To find the capacity of the tank, we need to determine how much water the tank can hold.
Let's assume the capacity of the tank is C liters.
When there is a leak in the bottom of the tank, it can empty the tank in 8 hours. This means that every hour, the leak can drain C/8 liters of water.
When a tap is open to the tank, it takes 12 hours to empty the tank. The tap admits 6 liters of water per hour, so in 12 hours, the tap has filled 12 * 6 = 72 liters of water.
Since the tank is emptying due to the leak and filling due to the tap at the same time, the effective draining rate per hour is (C/8) - 6 liters of water.
We can set up the equation:
(C/8) - 6 = 0
To solve for C, we can multiply both sides of the equation by 8:
C - 48 = 0
Adding 48 to both sides, we get:
C = 48
Therefore, the capacity of the tank is 48 liters.