Question

Q: A cistern has two pipes. The first and second pipes can fill the empty
cistern in 12 hours and 18 hours respectively. If both pipes are opened
together, how much time will the empty cistern need in order to be filled?​

Answer 1

Answer:

7 hours 12 minutes

Step-by-step explanation:

Time taken by first pipe to fill cistern = 12 hours

Since time and work are inversely proportional

Work done in 1 hour by first pipe = 1/12

Similarly

Work done in 1 hour by second pipe = 1/18

To find: time taken to fill cistern

Let the time taken be x.

Then, $x(\frac{1}{12} + \frac{1}{18})=1\\\frac{1}{12} + \frac{1}{18}= \frac{1}{x}$

$\frac{3 + 2}{36} = \frac{1}{x}$

5/36 = 1/x

x = 7.2 hours

= 7 hours 12 minutes

Therefore, it will take 7 hours and 12 minutes to fill the cistern.

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Answer 2

Answer:  I am giving a very simple, quick and the best solution

Step-by-step explanation:

Assume tank capacity as 36 lts (LCM of 12,18)

Pipe A fills 3 lts/hr individually

Pipe B fills 2 lts/hr individually

now both pipes are open hence tank can be filled at the rate of 5lts/hr

ans : time taken 36/5 =  7.2 hours