Question

The ratio of the tens digit to the ones digit of a $2$-digit number is $2:3$. If $27$ is added to the number, the digits interchange their places. Find the number.

Answer 1

Let the ones digit and tens digit of the number be $a,b$ respectively.

number $=ba$

given that,

$\frac{b}{a}=\frac{2}{3}$

$\to 3b=2a\to b=\frac{2a}{3}$ -------$\left(1\right)$

it is also given that,

$ba+27=ab$

$(10b+a)+27=10a+b$

$9a-9b=27$

$9(a-b)=27$

$a-b=3$

put the value of $b$ from equation $1$

$a-\frac{2a}{3}=3$

$3a-2a=9$

$a=9,b=\frac{2\times 9}{3}=6$

number $=69$