Question

A two digit number is 4 more than 6 times the sum of its digits.if 18 is subtracted from the number, the digits are reversed, find the number.​

Answer 1

GIVEN :-

• A two digit number is 4 more than 6 times the sum of digits .

• If 18 is subtracted from the number , the digits are reversed .

TO FIND :-

• The two digit number .

SOLUTION :-

   Let ,

   The digit in tens place = x

   The digit in ones place = y

   Two digit number = 10x + y

  According to the first condition ,

    $\longrightarrow\sf 10x+y = 4+6\times (x+y) \\\\\longrightarrow 10x+y = 4+6x+6y \\\\\longrightarrow 10x-6x+y-6y=4\\\\\longrightarrow 4x-5y=4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \.........................(1)$

 According to the second condition ,

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

  Eq (2) × 4 ,

    $\longrightarrow\sf 4x-4y = 8 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..............(3)$

  Eq (3) - Eq (1)  ,

    $\bf\longrightarrow y = 4$

 Substitute value of y in Eq (2) ,

   $\longrightarrow\sf x-4=2\\\\\longrightarrow x = 2+4\\\\\longrightarrow\bf x=6$

 Two digit number = 64