Pipe A can fill a tank in 13 hours, Pipe B in 27 hours, and Pipe C in 19 hours. What is the time (in hours) taken to fill the tank when all three pipes are opened together?

Correct option is C

Given:

Pipe A fills in 13 h, Pipe B in 27 h, Pipe C in 19 h.

Find time when all three run together.

Solution:
Combined rate =
​$$\frac{1}{t}=\frac{1}{13}+\frac{1}{27}+\frac{1}{19}$$​​

​$$=\frac{1111}{6669}$$​

t$$=\frac{6669}{1111}=6\frac3{1111}$$​​
Alternate Method:

Take LCM of (13,27,19) = 6669 units (capacity).
In 1 hour: A fills 6669/13=513 units, B = 247 units, C =351 units.
Together per hour =513 + 247 + 351=1111 units.
Time =$$\frac{6669}{1111}=6\frac3{1111}$$​ hours.