Pipe X can fill a tank 7 times faster in comparison to pipe Y. It takes 49 minutes for pipe X and Y to fill the tank together. How much time will pipe Y alone take to fill the tank?

Correct option is A

Given:

Pipe X is 7 times faster than pipe Y

Time taken by X and Y together = 49 minutes

Formula Used:
Let the time taken by pipe Y alone = y minutes
Then pipe X alone will take $$\frac{y}{7}$$ minutes​
Combined rate of work = sum of individual efficiency

Efficiency (Work Done Per Minute) = $$\frac{\text{Total Work}}{\text{Total time}}$$​​

​Solution:

Combined Efficiency = ​​$$\frac{1}{y} + \frac{1}{y/7} = \frac{1}{y} + \frac{7}{y} = \frac{8}{y}$$

$$\text{Time taken together} = \frac{1}{\text{Combined Efficiency}} = \frac{y}{8}$$

$$\Rightarrow\frac{y}{8} = 49$$​​​

​$$\Rightarrow y = 49 \times 8 = 392$$ minutes​

Time taken by pipe Y alone = 392 minutes

Thus, the correct option is (a) 392 minutes

Alternate:

​$$\frac{X}{Y}$$ = $$\frac{7}{1}$$

Total work = (7 + 1) $$\times$$ 49

=  8 $$\times$$ 49

= 392

Time taken by pipe Y alone = $$\frac{392}{1}$$

= 392 minutes.