Question

the ratio of tens digit to the unit digit of a two digit number is 2:3. if 27 is added to the number, the digits interchange their places, find the number

Answer 1

Let them be 2x and 3x
when we write it like a number we write
$2x \times 10 + 3x = 20x + 3x = 23x$
given
$23x + 27 = 32x \\ 27 = 32x - 23x \\ 27 = 9x \\ x = 27 \div 9 \\ x = 3 \\ 2x = 3 \times 2 = 6 \\ 3x = 3 \times 3 = 9$
so the number is 69
VERIFICATION
if we add 27 to 69 we get 96
so 69 is the correct answer