Three pipes A, B and C were opened to fill a tank. Working alone, A, B and C require 10, 15 and 20 hours respectively. A was opened at 7 AM, B at 8 AM and C at 9 AM. At what time the tank would be completely filled, given that pipe C can only work for 3 hours at a stretch, and needs 1 hour standing time to work again.

**(A)** 12 : 00 PM

**(B)** 12 : 30 PM

**(C)** 1 : 30 PM

**(D)** 1 : 00 PM

**Answer:** **(B)** **Explanation:** Let the capacity of the tank be LCM (10, 15, 20) = 60

=> Efficiency of pipe A = 60 / 10 = 6 units / hour

=> Efficiency of pipe B = 60 / 15 = 4 units / hour

=> Efficiency of pipe C = 60 / 20 = 3 units / hour

=> Combined efficiency of all three pipes = 13 units / hour

Till 9 AM, A works for 2 hours and B work for 1 hour.

=> Tank filled in 2 hours by A = 12 units

=> Tank filled in 1 hour by B = 4 units

=> Tank filled till 9 AM = 16 units

=> Tank still empty = 60 – 16 = 44 units

Now, all three pipes work for 3 hours with the efficiency of 13 units / hour.

=> Tank filled in 3 more hours = 39 units

=> Tank filled till 12 PM = 16 + 39 units = 55 units

=> Tank empty = 60 – 55 = 5 units

Now, C is closed for 1 hour and these remaining 5 units would be filled by A and B working together with the efficiency 10 units / hour.

=> Time taken to fill these remaining 5 units = 5 / 10 = 0.5 hours

Therefore, time at which the tank will be completely filled = 12 PM + 0.5 hours = 12 : 30 PM

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