Question

The difference between a two digit number and the number obtained by interchanging the digit is 36 . What is the difference between the sum and the difference of the digit of the number if the ratio between the digit of the number is 1:2 ? ​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

Let x be the unit digit and y be the tenth digit

So the original number is 10y + x

Now the number obtained by interchanging the digit is 10x + y

By the given condition 1

$(10y + x) - (10x + y) = 36$

$\implies \: 9y - 9x = 36$

$\implies \: y - x = 4 \: \:.........(1)$

By the given condition 2

$x: y \: = 1 : 2$

$\implies \: \displaystyle \: \frac{x}{y} = \frac{1}{2}$

$\implies \: y = 2x \: \: ......(2)$

From Equation (1) & Equation (2)

$2x - x = 4$

$\implies \: x = 4$

So

$y = 2x = 8$

So the original number is 84

Unit digit = 4

Tenth place = 8

So the sum of the digits = 8 + 4 = 12

Difference of the digits = 8 - 4 = 4

RESULT

Hence difference between the sum and the difference of the digit of the number

= 12 - 4

= 8