Two taps can fill a cistern in 2 hours and 54 hours respectively. A third tap can empty it in 54 hours. How long (in hours) will it take to fill the empty cistern, if all of them are opened together?

Correct option is C

Given:

First tap can fill the cistern in 2 hours,

Second tap can fill the cistern in 54 hours

Third tapcan empty the cistern in 54 hours 

Formula Used:  

If a Pipe fill a tank in x hours , 

Then work rate of pipe = $$\frac{1}{x}$$ ​

Solution: 

Work rate of first tap = $$\frac 1 2$$ 

Work rate of second tap = $$\frac{1} {54}$$ 

Work rate of third tap(empty) = ​$$\frac{1} {54}$$

Filling rate of the first and second taps:

​$$\text{Total filling rate} = \frac{1}{2} + \frac{1}{54}.$$​​​​

When all three taps are open, the combined rate of filling is:

Effective rate = $$\frac{1}{2} + \frac{1}{54} - \frac{1}{54}$$​​

Effective rate = $$\frac{1}{2}$$ 

Now , 

Time taken  to fill the tank =$$\frac{1}{\frac{1}{2}}$$​ = 2  hours.

It will take 2 hours to fill the empty cistern when all three taps are opened together.

Thus, the correct answer is option (c) 2