5Dec19 SS Q30

0. Three taps A, B and C can fill a tank in 8, 10 and 12 hours respectively. The tap A is open all the time continuously. But taps B and C are open for one hour each alternately. How long will it take the tank to be full?

  • Option : B
  • Explanation :
    Part of the tank filled in first hour by tap
    A and B = 1/8 + 1/10 = 9/40 tank
    Part of the tank filled in second hour by tap
    A and C = 1/8 + 1/12 = 5/24
    Part of the tank filled in 2 hours
    9/40 + 5/24 = 26/60 tank
    Part of the tank remains empty after 4 hours
    1 - [8 x (26/60)] = 2/15 tank
    Time required to fill 2/15 tank by tap A and B
    2/15 x 40/9 = 16/27 hour Hence, total time taken = 4 + (16/27) = 4(16/27)hours
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