Question

Consider a $2$-digit positive number $x$, with tens digit $t$ and units digit $u$. Let $y$ be the $2$-digit number formed by reversing the digits of $x$. Find the expression which is equivalent to $x-y$.

• A. $9(t-u)$
• B. $9(u-t)$
• C. $9t-u$
• D. $9u-t$
• E. $0$

Answer 1

The correct option is A $9(t-u)$

According to the question $x=10t+u$

If we reverse the digit of $x$, then $y=10u+t$

$\therefore x-y=(10t+u)-(10u+t)$

$\Rightarrow x-y=10t+u-10u-t$

$\Rightarrow x-y=9t-9u$

$\Rightarrow x-y=9(t-u)$