Correct Answer - Option 1 : 8
A can fill the tank in 24 minutes and B can fill the tank in 32 minutes.
So, A can fill 1 / 24 tank in 1 minute and B can fill 1 / 32 tank in 1 minute.
Now, both the pipes are opened simultaneously
Therefore, Their 1-minute work is
⇒ (1 / 24) + (1 / 32) = 7 / 96
Suppose both the pipes are opened for 'X' minutes.
Therefore, their 'X' minutes work will be (7 / 96) X
Now, the remaining work is 1 - (7 / 96) X
It is given that after X minutes pipe B will be closed and the remaining work will be done by pipe A only.
Therefore,
⇒ 1 - (7 / 96) X × 24 = 18 - X
⇒ (96 - 7X) / 4 = 18 - X
⇒ 3X = 24
⇒ X = 8 minutes
Therefore, after 8 minutes should B be closed so that the tank is full in 18 minutes.
Hence, the correct answer is 8 minutes.
