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      Question

      A and B together can finish a job in ‘x’ days, while

      A alone takes ‘x + 32’ days to complete it. B alone can finish the job in 90 days. If C is 20% more efficient than A, how many days will C alone take to complete the work?
      A 48 days Correct Answer Incorrect Answer
      B 50 days Correct Answer Incorrect Answer
      C 54 days Correct Answer Incorrect Answer
      D 60 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      According to question;

      1/(x + 32) + 1/90 = 1/x

      Or, x² + 122x = 90x + 2880

      Or, x² + 32x – 2880 = 0

      Or, x² + 72x – 40x – 2880 = 0

      Or, x(x + 72) – 40(x + 72) = 0

      Or, (x – 40)(x + 72) = 0

      So, x = 40, -72

      Number of days can’t be negative, so x = 40

      Time taken by A to complete the work = 40 + 32 =72 days


      Total work = 360 units (LCM of 40 and 72)

      Efficiency of A = 360/72 = 5 units per day

      Efficiency of C = 1.20 × 5 = 6 units per day

      Desired time = 360/6 = 60 days

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