Question

Three pipes A, B and C can fill a tank in 10, 15 and 20 hours respectively. Pipe A was opened at 6 AM, pipe B at 7 AM and pipe C at 8 AM. At what time was the tank completely filled?

• A. 11:20 AM
• B. 12:20 PM
• C. 11:30 AM
• D. 12:15 PM

Hint:

When pipes are opened at different times, calculate the work done in each interval until all pipes are working together. Then, calculate the time to finish the remaining work with the combined rate.

Answer 1

The Correct Option is A

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 = \(1 \times 6 = 6\) units. From 7 AM to 8 AM (1 hour): Pipes A and B work. Filled = \(1 \times (6+4) = 10\) 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 = \(6 + 4 + 3 = 13\) units/hour. Time to fill remaining part = \( \frac{\text{Remaining Work}}{\text{Combined Rate}} = \frac{44}{13} \) hours.

Step 4: Convert the time into hours and minutes and find the final time. \( \frac{44}{13} \text{ hours} = 3\frac{5}{13} \) hours. This is 3 hours and \( \frac{5}{13} \times 60 \) minutes = 3 hours and \( \approx 23 \) 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.