Question

The sum of the digits of a two-digit number is 9. If 9 is added to the number obtained by reversing the digits of this number, the result is 3 times the original number. Find the number.

• A. 27
• B. 36
• C. 45
• D. 81

Answer 1

The correct option is A 27

Let the 2-digit number be XY. Then, its expanded form is 10X + Y.
Also, the number obtained by reversing its digits is YX. whose expanded form is 10Y + X.
From the given data.
X + Y = 9...(i)
10Y + X + 9 = 3(10X + Y)
$\Rightarrow 10Y+X+9=30X+3Y$
$\Rightarrow 29X-7Y=\mathrm{9...}\left(ii\right)$

$7\left(i\right)+\left(ii\right)\Rightarrow 7X+7Y+29X-7Y=72$
$\Rightarrow 36X=72$
$X=2$
From (i), Y = 7

Thus, the required 2-digit number is 27.