**Pipe:**It is used to either fill the tank or empty the the tank.

**Tap:**It is also user for, either to fill the tank or to empty the tank.

**Tank or Cistern or Reservoir:**It is used to store the water.

**Inlet:**A pipe or a tap connected with a tank (or a cistern or a reservoir), if it fills it.

**Outlet:**A pipe or a tap connected with a tank (or a cistern or a reservoir), if it empties it.

Most of the rules are similar to time and work concepts:

Here we can assume, inlet is a person doing positive work and outlet is a person doing negative work.

- If a pipe can fill a tank in ‘a’ hour, then the part filled in 1 hr. = 1/a
- If two pipes can fill a tank in a and b hours respectively, then both together in 1 hr. can fill = 1/a + 1/b part of the tank.

They together can fill the tank in = (ab)/(a+b) time - If a pipe can empty a tank in b hour, then the part of the tank emptied in 1 hr. = 1/b
- If both pipes (one can fill in a hr. and another can empty in b hrs) are opened simultaneously (and 1/a>1/b), then, the net part filled in 1 hour = (part filled in 1 hr.) – (part emptied in 1 hr.)

= (1/a – 1/b)

Together they can fill the tank in = ab/(a-b) hours - If both pipes are opened simultaneously (and 1/b>1/a), then

the net part emptied in 1 hour = (part emptied in 1 hr.) – (part filled in 1 hr.)

= (1/b – 1/a)

Together they can fill the tank in = ab/(b-a) hours - Three pipes can fill (or empty) a cistern in x, y and z hours while working alone. If all the three pipes are opened together, the time taken to fill (or empty) the cistern is given by

= 1/(1/x+1/y+1/z) = xyz/xy+yz+xz hours - Two pipes can fill a cistern in x, y hours while working alone and a third pipe can empty the cistern in z hours. If all the three pipes are opened together, the time taken to fill (or empty) the cistern is given by

= 1/[(1/x)+(1/y)-(1/z)] = xyz/yz+xz-xy hours

{we can remember the –ve sign by as 1/x+1/y-1/z, so with z numerator will be xy, so with xy it will be –ve}

**Example 1.** A pipe takes 12 min. to fill 3/4^{th} of a tank. How much time it will take to fill the half of the tank?

Explanation:

3/4th of pipe is filled in = 12 min

Full tank can be filled in = 12/(3/4) = 12*4/3 16 min

half of the tank will be filled in = 16*(1/2) = 8 min.

**Example 2.** Two pipes can fill a reservoir in 20 and 30 mins working alone respectively. If both pipes opened at a time, find the time when the reservoir will be filled fully.

Explanation:

In 20 min pipe#1 fill = 1 reservoir

In 1 min pipe#1 fill = 1/20 part

In 30 min pipe#2 empty = 1 reservoir

In 1 min pipe#2 empty = 1/30 part

In 1 min overall filled (both pipes opened) = 1/20 – 1/30 = 1/60 part

=> 1/60 part is filled in = 1 min

1 full reservoir can be filled in = 60 min

**Example 3.** Two Pipes A and B can fill a tank in 15 and 18 min alone respectively. A hole in the tank takes 90 min to empty it. In how much time the tank will be emptied, if both pipes and hole are opened simultaneously?

Explanation:

In 1 min = (1/15 + 1/18 – 1/ 90) = 1/9 part is filled

=> The tank can be emptied in 9 min.

**Example 4.** There are two tapes in a reservoir, named A and B. Tab A takes 20 min and B 40 min to fill the tank fully alone. Both the taps are opened simultaneously. Tap A was closed after 10 min. In how much more time will the reservoir be full?

Explanation:

Part filled by both A and B in 1 min = 1/20 + 1/40 = 3/40

Part filled by both in 10 min = 10*3/40 = 3/4

Part left empty = 1-3/4 = 1/4

Now 1/4 part has to fill by pipe B alone,

B fill 1 reservoir in 40 min

1/4 part reservoir can be filled in = 40*1/4 = 10 min

=> Total time taken to fill the tank = 10 min together + 10 min B alone

= 20 min