Question

The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. Then the number is ___.

• A. 27
• B. 72
• C. 63
• D. 36

Answer 1

The correct option is D

36

Let the digits in the tens place be $x$ and digit in the ones place be $y$.

Sum of the digit is 9

Therefore, we have

$x+y=9$ ...(1)

The two digit number is of the form $10x+y$.

$\therefore$ We have $10x+y+27=10y+x$

$\Rightarrow 9x-9y=-27$

$\Rightarrow x-y=-3$ ...(2)

On subtracting equation (2) from (1) and eliminating y, we get

$2x=6\Rightarrow x=3$

On substituting value of x in equation (1), we get

$x+y=9$

$3+y=9$

$y=6$

So, $10x+y$ = $10\times 3+6=36$

Therefore, the two digit number is 36.