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A leak in the bottom of a tank can empty the full tank in 7 hours. An inlet pipe fills water at the rate of 2 litres a minute. When the tank is full the inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank in litres is
  • a)
    3450 litres
  • b)
    5460 litres
  • c)
    7620 litres
  • d)
    6720 litres
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A leak in the bottom of a tank can empty the full tank in 7 hours. An ...
In 1 hr = 1/7 – 1/8 = 8-7/56 = 1/56
In 1 min = 1/(56*60) = 1/3360
Inlet pipe fill water at the rate of 2 liters a minute = 2*3360 = 6720litres
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Most Upvoted Answer
A leak in the bottom of a tank can empty the full tank in 7 hours. An ...
In 1 hr = 1/7 – 1/8 = 8-7/56 = 1/56
In 1 min = 1/(56*60) = 1/3360
Inlet pipe fill water at the rate of 2 liters a minute = 2*3360 = 6720litres
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Community Answer
A leak in the bottom of a tank can empty the full tank in 7 hours. An ...
Problem: A leak in the bottom of a tank can empty the full tank in 7 hours. An inlet pipe fills water at the rate of 2 litres a minute. When the tank is full the inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank in litres is

Solution:

Let the capacity of the tank be 'x' litres.

Given, leak can empty the full tank in 7 hours.

Hence, leak empties 1/7th of the tank in 1 hour.

Let the inlet pipe take 'y' hours to fill the full tank.

Hence, the inlet pipe fills (2*60*y) litres of water in y hours.

When the tank is full, the inlet and the leak are open.

Hence, the net outflow of water from the tank is (1/7 - 1/8) of the tank in 1 hour.

[(8-7)/56]x = x/56

Hence, the inlet pipe fills x/56 litres of water in 1 hour.

Therefore, the inlet pipe fills (x/56)*y litres of water when the tank is full.

But the net outflow of water is equal to the inflow of water.

Hence, (x/56)*y = (1/7 - 1/8)*x

=> y = 48

Therefore, the capacity of the tank is x = (2*60*48)/(1/7)

=> x = 6720 litres

Hence, the correct option is D.
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A leak in the bottom of a tank can empty the full tank in 7 hours. An inlet pipe fills water at the rate of 2 litres a minute. When the tank is full the inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank in litres isa)3450 litresb)5460 litresc)7620 litresd)6720 litrese)None of theseCorrect answer is option 'D'. Can you explain this answer?
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