There are two inlets and one outlet to a tank. Inlet A and B take 1.5 hours and 2 hours respectively to fill the tank. While outlet C can empty the entire tank in 30 minutes. The gardener decides to open Inlet A at 8 am when he arrives on duty and Inlet B one hour later. Outlet C is opened at 10 am. What will be the time by his watch when the tank will be entirely empty again?

Let the tank get empty in T hours counting from 8 am.
A is on for T hours and work is done by A = Work in 1-hour × T hours = T/1.5 = 2T/3

Similarly, B starts at 9 am i.e. it's on for (T-1) hours & work done is = (T - 1)/2

Similarly, C starts at 10 am i.e. it's on for (T-2) hours & work done is = (T - 2)/(1/2) = 2(T - 2)

Initially, the tank is empty and after T hours too, it is empty. So, the total work done is 0.

According to the question,
2T/3 + (T - 1)/2 - 2(T - 2) = 0
⇒ (4T + 3T - 3 - 12 T + 24)/6 = 0
⇒ -5T + 21 = 0
⇒ 5T = 21
⇒ T = 21/5
= 4.2 hours = 4 hours 12 minutes5
This time is needed for the tank to get empty.
The exact time will be 4 hours 12 min from 8 am = 12.12 pm