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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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