Answer :
To find out when the auxiliary pump should be turned on, we can follow these steps:
1. Determine the rate of work of each pump. The main pump can empty the tank in 5 hours, so its work rate is 1/5 tank per hour. The auxiliary pump can empty the tank in 10 hours, so its work rate is 1/10 tank per hour.
2. Since both pumps are working together to empty the tank, their combined work rate is the sum of their individual work rates. Therefore, the combined work rate is 1/5 + 1/10 = 3/10 tank per hour.
3. Calculate the time it takes for both pumps to empty the tank together. The main pump starts at 10:00 a.m. and needs to work until 2:00 p.m., which is 4 hours.
4. Let x be the time the auxiliary pump needs to work. The equation to represent the total work done by both pumps is (4 hours) * (3/10) + x * (1/10) = 1 tank (since they need to empty the tank together).
5. Solve for x by substituting the known values into the equation. You should get x = 2 hours.
6. If the main pump starts at 10:00 a.m. and works for 4 hours, then the auxiliary pump should be turned on 2 hours before the end to work for 2 hours. This means the auxiliary pump should be turned on at 12:00 p.m.
Therefore, the correct answer is (A) 12:00 p.m.
