Question

The sum of digits of a two digit number is $8$ and the difference between the number and that formed by reversing the digits is $18$. What is the difference between the digits of the number?

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (B)

$2$

Let the $2$ - digit number of $\stackrel{T}{x}\stackrel{O}{y}$
$x+y=8$ where T and O are tens place and ones place
$\stackrel{T}{x}\stackrel{O}{y}-\stackrel{T}{y}\stackrel{O}{x}=18$
$\Rightarrow (10x+y)-(10y+x)=18$
$\Rightarrow 9x-9y=18$
$\Rightarrow 9(x-y)=18$
$\Rightarrow x-y=2$
Therefore, difference between digits is $2$.