Tap A, B and C can fill a tank in 16 hours, 12 hours and 20 hours respectively. The three taps are opened alternately for 1 hour each, starting with tap A at 7 am, B at 8 am and so on. At what time will the tank get filled?

Sure, let's solve this step by step.

Step 1: Find out how much of the tank each tap can fill in one hour.

• Tap A can fill 1/16 of the tank in one hour.
• Tap B can fill 1/12 of the tank in one hour.
• Tap C can fill 1/20 of the tank in one hour.

Step 2: Find out how much of the tank the three taps can fill in three hours (since they are opened alternately for 1 hour each).

• In three hours, the taps can fill 1/16 + 1/12 + 1/20 = 15/240 + 20/240 + 12/240 = 47/240 of the tank.

Step 3: Find out how many complete cycles of 3 hours are needed to fill the tank.

• The number of complete cycles needed is obtained by dividing 1 (the whole tank) by 47/240 = 240/47 ≈ 5.1. Since we can't have a fraction of a cycle, we round this up to 6 cycles.

Step 4: Calculate the total time taken for these complete cycles.

• The total time taken for 6 cycles is 6 * 3 = 18 hours.

Step 5: Find out how much of the tank is filled after these complete cycles.

• After 6 cycles, 6 * 47/240 = 282/240 = 1.175 of the tank is filled. This is more than 1, so the tank is already filled before the 6th cycle is completed.

Step 6: Find out at what time the tank gets filled.

• The taps started at 7 am and 18 hours later, it's 1 am the next day. But since the tank got filled during the 6th cycle, we need to subtract the extra time. In the 6th cycle, tap A would have been opened, and since tap A can fill 1/16 of the tank in one hour, it would have taken (1 - (5 * 47/240)) * 16 = 0.85 hours ≈ 51 minutes to fill the remaining part of the tank. So, the tank got filled at around 12:09 am.