Explanation:

- Tap A can fill the tank in 10 hours, so it fills 1/10 of the tank in one hour.

- Tap B can fill the tank in 12 hours, so it fills 1/12 of the tank in one hour.

- Together, the two taps fill 1/10 + 1/12 = 11/60 of the tank per hour.

- They need to fill the entire tank by 4 p.m. if they start at 10 a.m., which is a total of 6 hours.

- In 6 hours, both taps together will fill 6 * (11/60) = 11/10 of the tank.

- To fill the tank exactly, some time before 4 p.m., tap A should be closed.

- Let x be the number of hours after 10 a.m. tap A is open.

- Then tap B will work for the entire 6 hours, filling 6 * (1/12) = 1/2 of the tank.

- The remaining 1/2 of the tank must be filled by tap A in x hours: x * (1/10) = 1/2.

- Solving gives x = 5 hours.

- Tap A should be closed 5 hours after 10 a.m., that is, at 3 p.m.

Option 2, 3 p.m. is correct.