Important Formulas of Pipes and Cistern

  1. Inlet:A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.Outlet:

    A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.

  2. If a pipe can fill a tank in x hours, then:
    part filled in 1 hour = 1 .
    x
  3. If a pipe can empty a tank in y hours, then:
    part emptied in 1 hour = 1 .
    y
  4. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then
    the net part filled in 1 hour = 1 1 .
    x y
  5. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where x > y), then on opening both the pipes, then
    the net part emptied in 1 hour = 1 1 .
    y x

1. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?

2. A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is

3. Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:

4.A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?

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