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      Question

      A student calculates the average of five two-digit numbers.

      If one of them is reversed and the new average increases by 9, and all the numbers are consecutive multiples of 12, then what is the reversed number?
      A 15 Correct Answer Incorrect Answer
      B 32 Correct Answer Incorrect Answer
      C 27 Correct Answer Incorrect Answer
      D 95 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the number which is reversed be (10a + b)

      Then reversed = (10b + a)

      As per question:

      10b + a – 10a – b = 9 × 5

      ⇒ 9(b – a) = 45

      ⇒ b – a = 5

      Now checking five consecutive multiples of 12:

      24, 36, 48, 60, 72

      Try 27 → reversed = 72

      So the number which is reversed is 27

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