Question

Three pipes a and b and c can fill a swimming pool in 6 hours. After working on it together for 2 hours,C is closed and A and B finish the remaing work in 7 hours. Find the time taken by alone to fill the swimming pool.

Answer 1

The pipe C alone can fill the tank in 14 hours .

Explanation:

Given as :

The three pipes a , b , c can fill the pipes in 6 hours

They work for 2 hours

After that c pipe is close and a , b finish remaining work

Now, According to question

In 1 hour pipes ( a + b + c ) fill
`(1)/(6)` of the tank

∴ In 2 hour pipes ( a + b + c ) fill
`(2)/(6)` =
`(1)/(3)` of the tank

Remaining ( 1 -
`(1)/(3)` ) =
`(2)/(3)` part is filled by pipes a and b in 7 hours

∴ The whole tank is filled by a and b in 7 ×
`(3)/(2)` =
`(21)/(2)` hours

∴ In 1 hour pipes A and b fill the tank in
`(2)/(21)` hours

∴ In 1 hour pipes C alone can fill the tank in
`(1)/(6)` -
`(2)/(21)` hours

Or, In 1 hour pipes C alone can fill the tank in
`(9)/(126)` =
`(1)/(14)`

Or, In 1 hour pipes C alone can fill the tank in 14 hours

Hence The pipe C alone can fill the tank in 14 hours . Answer