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  • Question
  • Three taps P, Q and R can fill a tank in 12 hrs, 15 hrs and 20 hrs respectively. If P is open all the time and Q and R are open for one hour each alternately, starting with Q, then the tank will be full in how many hours ?


  • Options
  • A. 9 hrs
  • B. 7 hrs
  • C. 13 hrs
  • D. 11 hrs

  • Correct Answer
  • 7 hrs 

    Explanation

    Given,

    P can fill in 12 hrs

    Q can fill in 15 hrs

    R can fill in 20 hrs

    => Volume of tank = LCM of 12, 15, 20 = 60 lit

    => P alone can fill the tank in 60/12 = 5 hrs

    => Q alone can fill the tank in 60/15 = 4 hrs

    => R alone can fill the tank in 60/20 = 3 hrs

    Tank can be filled in the way that

    (P+Q) + (P+R) + (P+Q) + (P+R) + ....

    => Tank filled in 2 hrs = (5+4) + (5+3) = 9 + 8 = 17 lit

    => In 6 hrs = 17 x 6/2 = 51 lit

    => In 7th hr = 51 + (5+4) = 51 + 9 = 60 lit

    => So, total tank will be filled in 7 hrs.

  • Tags: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO

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