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Maths

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The sum of the 2digits of a 2 digit number is 15. If th number formed by reversing the digits is less than the orginal number by 27.Find the orginal number

  • Maths - ,

    Let the number be ab

    a+b=15
    10b+a = 10a+b - 27

    a + b = 15
    -9a + 9b = -27

    a + b = 15
    a - b = 3

    2a = 18
    a=9
    b=6

    check: 69 = 96 - 27

  • Maths - ,

    Answering by logic and mental calculations:

    Since the order of digits is not important (they will be reversed anyway), the only two-digit combinations that add up to 15 are (8,7) and (6,9).
    (8,7) does not work because 87-78=9. Now try 96-69=27, which is obviously the answer.

  • Maths - ,

    When we have a two digit number, it can be expressed as :

    10 a + b


    In this case :

    10 a + b = orginal number


    The sum of the 2 digits is 15

    a + b = 15 Subtract a to both sides

    a - a + b = 15 - a

    b = 15 - a


    If you reverse the digits of 10 a + b, it will be :

    10 b + a


    10 b + a = orginal number - 27 Add 27 to both sides


    10 b + a + 27 = orginal number - 27 + 27

    10 b + a + 27 = orginal number

    10( 15 - a ) + a + 27 = orginal number

    150 - 10 a + a + 27 = orginal number

    177 - 9 a = orginal number


    Also


    10 a + b = orginal number


    10 a + 15 - a = orginal number

    9 a + 15 = orginal number


    177 - 9 a = 9 a + 15 Subtract 15 to both sides


    177 - 9 a - 15 = 9 a + 15 - 15

    162 - 9 a = 9 a Add 9 a to both sides

    162 - 9 a + 9 a = 9 a + 9 a

    162 = 18 a Divide both sides by 18

    162 / 18 = a

    9 = a

    a = 9


    b = 15 - a

    b = 15 - 9 = 6

    orginal number = 10 a + b = 10 * 9 + 6 = 90 + 6 = 96

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