Pipe A can fill a tank in 13 hours, pipe B can fill the same tank in 26 hours and pipe C can fill the same tank in 17 hours. The time taken by them to fill the same tank if they operate together is:

Correct option is D

​$$\textbf{Given:} \\\text{Time taken by Pipe A} = 13 \text{ hours} \\\text{Time taken by Pipe B} = 26 \text{ hours} \\\text{Time taken by Pipe C} = 17 \text{ hours} \\\\\textbf{Formula Used:} \\\text{Total Work} = \text{LCM of given times} \\\text{1-hour work} = \dfrac{\text{Total Work}}{\text{Time}} \\\text{Time} = \dfrac{\text{Total Work}}{\text{Total 1-hour work}} \\\\\textbf{Solution:} \\\text{LCM of } 13, 26, 17 = 442 \\\\\text{Total work} = 442 \text{ units} \\\\\text{1-hour work of Pipe A} = \dfrac{442}{13} = 34 \text{ units} \\\\\ \\\text{1-hour work of Pipe B} = \dfrac{442}{26} = 17 \text{ units} \\\\\text{1-hour work of Pipe C} = \dfrac{442}{17} = 26 \text{ units} \\\\\text{Total 1-hour work together} = 34 + 17 + 26 = 77 \text{ units} \\\\\text{Required time} = \dfrac{442}{77} \\= \dfrac{442}{77} \\= 5 \frac{57}{77} \text{ hours}$$​​