CAT Exam Model Paper 1 with solutions for free online practice

A cylindrical overhead tank is filled by two pumps-P${}_1$ and P${}_2$. P${}_1$ can fill the tank in 8 h while P${}_2$ can fill the tank in 12 h. There is a pipe P${}_3$ which can empty the tank in 8 hours. Both the pumps are opened simultaneously. The supervisor of the tank, before going out on a work, sets a timer to open P${}_3$ when the tank is half filled so that tank is exactly filled up by the time he is back. Due to technical fault P${}_3$ opens when the tank is one third filled. If the supervisor comes back as per the plan what per cent of the tank is still empty?