Question

Q-1-The sum of the digits of a two digit number is 12.If the new number formed by reversing the digits is greater than the original number by 18 , find the original number.check your solution.

Answer 1

GIVEN :-

• Sum of digits of a two digit number is 12 .

• New number formed be reversing the digits is greater than

       the original number by 18 .

TO FIND :-

• Original number .

SOLUTION :-

  Let ,

   Digit in ten's place = x

   Digit in one's place = y

   Original number = 10x + y

   According to the first condition ,

    $\longrightarrow\sf x+y = 12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(1)$

   According to the second condition ,

   $\longrightarrow\sf10x+y+18= 10y+x \\\\\longrightarrow 10x-x+y-10y = -18\\\\\longrightarrow 9x-9y = -18\\\\\longrightarrow x-y =-2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..................(2)$

  Equation (2) + Equation (1) ,

   $\longrightarrow \sf 2x = 10 \\\\\longrightarrow x = 5$

 

 Substitute x = 5 in equation (1)

   $\longrightarrow\sf 5+y =12 \\\\\longrightarrow y = 7$

Original number = 57