Question

6. Pipe A can fill a tank in 5 hours. Pipe B in 10
hours and pipe C in 30 hours. If all the pipes
are opened, in how many hours will the tank be
filled?​

Answer 1

Answer:

If all Three pipes are opened at the same time the tank will get filled in 3 Hours.

Step-by-step explanation:

Given

$\bigstar$ Pipe A can fill the tank in 5 hours.

$\bigstar$ Pipe B  can fill the tank in 10 hours .

$\bigstar$ Pipe C  can fill the tank in 30 hours.

SOLUTION

$\sf Part\: of \:the\: tank \:that\: is \:filled \:by \: Pipe \:A = \frac{1}{5}$

$\sf Part\: of \:the\: tank \:that\: is \:filled \:by \: pipe\: B = \frac{1}{10}$

$\sf Part\: of \:the\: tank \:that\: is \:filled \:by \: pipe\: C = \frac{1}{30}$

$\sf Parts\; of \;tank \;filled\; by \;all\; three \;pipes\; i.e\; A,B \;and\; C\; in \;an\; Hour = \frac{1}{5} + \frac{1}{10} +\frac{1}{30}$

$\bigstar$ LCM of 5, 10 and 30 is  30

A+B+C =   1×6+1×3+1×1  

                       30

             =  6+3+1  

                  30

                 =  $\frac{10}{30} = \frac{1}{3}$

∵   Part of tank filled by Pipes A+B+C in one hour = 1/3

∴ Time taken by all three pipes to fill the tanks  = Reciprocal of 1/3 = 3 hrs