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A number consists of three digits …

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A number consists of three digits whose sum is 17. The middle one exceeds the sum of the other two numbers by 1.If the digits be reversed the number is diminished by 396.Find the number

    • Posted by Sai Vignesh 6 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 6 months ago

    Let digit at unit’s place = x and digit at hundred’s place = y
    {tex}\therefore{/tex} Middle digit ={tex} x + y + 1{/tex}
    Number = {tex}100y + 10(x + y + 1) + x{/tex}
    Number obtained by reversing the digits = {tex}100x + 10(x + y + 1) + y{/tex}
    ATQ.,
    {tex}x + y + (x + y + 1) = 17{/tex}
    {tex}\Rightarrow{/tex} {tex}2x + 2y = 16{/tex} ..(i)
    and {tex}100x + 10(x + y + 1) = x - 396{/tex} ..(ii)
    {tex}\Rightarrow{/tex} {tex}99x - 99y = -396{/tex}
    {tex}\Rightarrow{/tex} {tex}x - y = -4{/tex}
    By Solving equation (i) and (ii), we get
    x = 2, y = 6 and Number = 692

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