Three pipes A, B and C can fill a cistern in 10, 12 and 15 hours, respectively, while working alone. If all the three pipes are opened together, the times taken to fill the cistern will be

A 4 hours

B 6 hours

C 7 hours

D 5 hours

E None of these

Correct Answer: Option A

Since, three pipes A, B and C can fill a cistern in 10, 12 and 15 hours

∴ Part of the tank filled by Pipe A in 1 hour = 1/10

∴ Part of the tank filled by Pipe B in 1 hour = 1/12

∴ Part of the tank filled by Pipe C in 1 hour = 1/15

∴ Part of the tank filled by all three pipes in 1 hour \(= \frac{1}{{10}} + \frac{1}{{12}} + \frac{1}{{15}} = \frac{{15}}{{60}} = \frac{1}{4}\)

∴ Time taken to fill the cistern =4/1=4 hours