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math

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when you reverse the digits of the number 13,the number increases by 18.how many other 2digit numbers increase by 18 when their digits are reversed ?

  • math -

    let the unit digit be x and the tens digit be y
    then the number is 10y + x
    and the number reversed would be 10x + y
    but 10x + y - (10y + x) = 18
    9x - 9y = 18
    x-y = 2

    this works for:
    3,1 ---> our given case
    4,2
    5,3
    6,4
    7,5
    8,6
    and 9,7

    check 7,5
    if x=7, y = 5
    the original number was 57
    number reversed 75
    and 75 - 57 = 18

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