In pipes and water tank we will learn how
to solve different types of problems. A water tank or a cistern is connected
with two types of pipes to fill and empty it. The pipe which fills the tanks up
is called the **inlet**. The pipe which
empties it is called the **outlet**.

Suppose, if an inlet fills up the cistern in 5 hours, then in 1 hour it fills up 1/5 th part of it. We say that the work done by inlet in 1 hours is 1/5.

Similarly, if an outlet empties out the cistern in 4 hours, then in 1 hour it empties out 1/4 th part of the cistern. We say that the work done by the outlet in 1 hour is 1/4.

Now we will apply the concept of solving some real-life problems on pipes and a water tank or a cistern.

Word problems on pipes and water tank or cistern:

**1.** A cistern can be filled by a tap in 5 hours by the other tap in 4 hours. If both taps are opened together how long will it take to fill the cistern?

**Solution: **

Time taken by the 1st tap to fill the cistern = 5 hours

Therefore, work done by the 1st tap in 1 hour = 1/5

Time taken by the 2nd tap to fill the cistern = 4 hours.

Therefore, work done by the 2nd tap in 1 hour = 1/4

Therefore, work done by the both taps in 1 hour = 1/4 + 1/5

= (4 + 5)/20

= 9/20

Therefore, both taps will fill the cistern in = 20/9 hours.

**2.**
A tank can fill by the taps in 8 hours and can be emptied by the other taps in
10 hours. How long will it take to fill the tank if both the taps are opened
together?

**Solution:
**

Time taken by the 1st tap to fill the tank = 8 hours

In 1 hour, the tap fills 1/8 of the tank.

Time taken by the other tap to empty the tank = 10 hours

In 1 hour, the other tap empty -1/10 of the tank (since, empty is taken as negative)

Therefore, in 1 hour work done by tap A and tap B = 1/8 – 1/10

= (5 – 4)/ 40

= 1/40

Therefore, both the taps when opened together will fill the tank in 40 hours.

**3.**
A tank can be filled by one tap in 4 hour and empty by an outlet pipe in 6
hours. How long will it take to fill the tank if both the tap and pipe are
opened together?

**Solution:**

Time taken by tap to fill the tank = 4 hours

In 1 hour, the tap fill 1/4 th part of tank.

Time taken by pipe to empty the tank = 6 hours

In 1 hour, the pipe empties 1/6 th part of the tank.

Thus, in one hour (1/4 – 1/6) th = (3 – 2)/12) th

= 1/12 th part of the tank is filled.

Therefore, the tank will be filled in 12 hours.

Calculate Time to Complete a Work

Calculate Work Done in a Given Time

Problems on Time required to Complete a Piece a Work

Problems on Work Done in a Given Period of Time

Problems on Pipes and Water Tank

**7th Grade Math Problems**

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