Question

Pipes A, B and C can fill a tank in 8, 12 and
16 hours respectively. If all three pipes
are opened together, in how much time
will the tank be full?​

Answer 1

It will take 3 $\frac{9}{13}$ hours to fill the tank.

Step-by-step explanation:

It is given that,

Pipe A can fill the tank in 8 hours.

Pipe B can fill the tank in 12 hours.

Pipe C can fill the tank in 16 hours.

Hence,

In 1 hour pipe A can fill 1/8 part of  the tank.

In 1 hour pipe B can fill 1/12 part of the tank.

In 1 hour pipe C can fill 1/16 part of the tank.

∴ In 1 hour pipes A,B, and C can together fill_

(1/8) + (1/12) + (1/16)

= (6+4+3)/48 [∵ The L.C.M. of the denominators is 48.]

= 13/48 part of the tank.

13/48 parts of the tank can be filled in 1 hour

∴ 1 part of the tank can be filled in (48/13) hour

                                                       = 3 $\frac{9}{13}$ hours.