Question

The sum of the digits of a two digit number is $10$. If the digits are reversed, the new number is $72$ more than the original. Find the reversed number.

• A. $90$
• B. $91$
• C. $92$
• D. $93$

Answer 1

The correct option is B $91$

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 $=x+y=10$......(1)

And $10x+y=10y+x+72$

$\Rightarrow 9x-9y=72$

$\Rightarrow x-y=8$, divide both sides by $9$

$\Rightarrow x-(10-x)=8$, use (1)

$\Rightarrow 2x=8+10=18$

$\Rightarrow x=9$, so $y=1$

Hence the reversed number is $=10x+y=10\times 9+1=91$