Question

A number consists of two digits. The sum of the digits is $11$, reversing the digits, the number decreases by $45$. The number is

• A. $38$
• B. $65$
• C. $74$
• D. $83$

Answer 1

The correct option is D $83$

Let the number be $10x+y$
$x+y=11$ also $10y+x=45=10+y\Rightarrow 9y-9x=-45$
$\Rightarrow y-x=-5\Rightarrow x+y=11\Rightarrow 2y=6\Rightarrow y=3\Rightarrow x=8$
$\therefore$ Number is $83$