Question

Sum of the digits of a two digit number is $9$. When we interchange the digits, it is found that the resulting new number is greater than the original by $27$. What is the two digit number?

• A. $63$
• B. $36$
• C. $23$
• D. $32$

Answer 1

Answer: (B)

$36$

Let the two digit number be $x$ and $y.$

$x+y=9⟶\left(i\right)\therefore (10x+y)-(10y+x)=27,\Rightarrow 9x-9y=27\Rightarrow 3x-3y=9\Rightarrow x-y=3⟶\left(ii\right)$

By solving $\left(i\right)$ and $\left(ii\right)$

$2x=12$

$x=6$

By putting $x$ in $\left(i\right)$ , $y=3$

$\therefore n=36$