Question

The sum of digits of two digit number is $11$. If the new number formed by reversing the digits, is more than the original number by $9$. Then find the original number.

• A. $55$
• B. $60$
• C. $56$
• D. $70$

Answer 1

The correct option is C $56$

Let the unit's place number be $x$ and the tenth place number be $y$ of the two digit number

So the number will be $10y+x$

And the number formed by reversing the digits will be $10x+y$

Now given, sum of digits $=x+y=11$......(1)

And $10x+y=10y+x+9$

$\Rightarrow 9x-9y=9$

$\Rightarrow x-y=1$

$\Rightarrow x-(11-x)=1$, use (1)

$\Rightarrow 2x=1+11=12$

$\Rightarrow x=6$, so $y=5$

Hence the original number is $=10y+x=10\times 5+6=56$