Pipe And Cistern

Step 1: Use the LCM method to find the capacity and rates. Let the capacity of the tank be LCM(10, 15, 20) = 60 units. Rate of A = 60/10 = 6 units/hour. Rate of B = 60/15 = 4 units/hour. Rate of C = 60/20 = 3 units/hour.

Step 2: Calculate the units filled before all three pipes are open (i.e., by 8 AM). From 6 AM to 7 AM (1 hour): Pipe A works alone. Filled = units. From 7 AM to 8 AM (1 hour): Pipes A and B work. Filled = units. Total filled by 8 AM = 6 + 10 = 16 units.

Step 3: Calculate the remaining work and the time required to complete it. Remaining capacity = Total Capacity - Filled = 60 - 16 = 44 units. From 8 AM onwards, all three pipes are open. Combined rate = units/hour. Time to fill remaining part = hours.

Step 4: Convert the time into hours and minutes and find the final time. hours. This is 3 hours and minutes = 3 hours and minutes. The time to fill the tank after 8 AM is approximately 3 hours and 23 minutes. Final Time = 8:00 AM + 3 hours 23 minutes = 11:23 AM. The closest option is 11:20 AM.