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A two digit no. Is such …

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A two digit no. Is such that the product of its digits is 15 if 8 is added to the no. The digit interchange their place find the no.

    • Posted by Lucky? Dangi 6 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 6 months ago

    Assume digit at ten’s place = x and digit at unit’s place =  y
    ​​Therefore number = 10x + y
    Also xy = 15 {tex}\Rightarrow{/tex} x = {tex}\frac{15}{y}{/tex} ...(i)
    According to given situation we have, 
        10x + y + 18 = 10y + x
    {tex}\Rightarrow{/tex}9x - 9y + 18 = 0
    {tex}\Rightarrow{/tex}x - y + 2 = 0
    {tex}\Rightarrow{/tex}{tex}\frac{15}{y}{/tex} - y + 2 = 0 (From (i))
    {tex}\Rightarrow{/tex}15 - y2 + 2y = 0
    {tex}\Rightarrow{/tex}y2 - 2y - 15 = 0

    On factorizing the above quadratic equation we get
           (y - 5) (y + 3) = 0
    {tex}\Rightarrow{/tex}y = 5, y = -3 [ y = -3 is  rejected]
    Put the value of y = 5 in equation (i), we obtain
         x = {tex}\frac{15}{5}{/tex} = 3
    {tex}\therefore{/tex} Number = 3 {tex}\times{/tex} 10 + 5 = 35.

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