Question

two digit nom is obtained by either multiplying the sum of digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16, and then adding 3, find the number​

Answer 1

GIVEN :-

• Two digit number is obtained by multiplying the sum of digits

         by 8 and then subtracting 5 .

• The same two digit number is obtained by multiplying the difference

        of the digits by 16 , and then adding 3 .

TO FIND :-

• The two digit number .

SOLUTION :-

    Let ,

    Digit in tens place = x

    Digit in ones place = y

    The two digit number = 10x + y

    According to the first condition ,

      $\longrightarrow\sf10x+y= (x+y)\times 8 -5 \\\\\longrightarrow 10x+y=8x+8y-5 \\\\\longrightarrow 10x-8x+y-8y=-5\\\\\longrightarrow 2x-7y=-5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(1)$

   According to the second condition ,

    $\longrightarrow\sf 10x+y = (x-y)\times 16+3\\\\\longrightarrow 10x+y = 16x-16y+3\\\\\longrightarrow 16x-10x-16y-y=-3 \\\\\longrightarrow 6x-17y = -3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(2)$

  Eq (1) × 3 ,

       

    $\longrightarrow\sf 6x-21y=-15 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(3)$

  Eq (2) - Eq (3)  ,

     $\longrightarrow \sf 4y= 12 \\\\\longrightarrow\bf y = 3$

  Substituting y = 3 in eq (1) ,

     $\longrightarrow\sf 2x-7\times 3= -5 \\\\\longrightarrow 2x - 21 = -5 \\\\\longrightarrow 2x = -5+21 \\\\\longrightarrow 2x = 16 \\\\\longrightarrow\bf x = 8$

  TWO DIGIT NUMBER = 83