Question

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

• A. 27
• B. 72
• C. 63
• D. 36

Answer 1

The correct option is D

36

Let the digit in the ten's place be $x$ and digit in the unit's place be $y$

Sum of the digit is 9 ;therefore we have

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

The number = $10x+y$ ; when digits are reversed, the number becomes $10y+x$ ;

$\therefore$ we have,

$10x+y+27=10y+x\Rightarrow 9x-9y=-27$

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

Adding (2) and (1) we get,

$2x=6\Rightarrow x=3andy=6.$

Therefore the number formed is 36.