Question

the sum of digit of a two digit number is 15 if the number formed by reversing the digit is less than the original number by 27 find the original number

Answer 1

let first digit be x
second be y
when writing as a two digit number we write it like
$10x + y$
given
$10y + x = 10x + y - 27 \\ 10y + x - 10x - y = 27 \\ 9y - 9x = 27 \\ 9(y - x) = 27 \\ y - x = 27 \div 9 \\ y - x = 3$
now
$x + y = 15 \\ y - x = 3 \\ x + y + y - x = 15 + 3 \\ 2y = 18 \\ y = 18 \div 2 \\ y = 9$
now
$x + y = 15 \\ x + 9 = 15 \\ x = 15 - 9 \\ x = 6$
so number is
$10x + y = 10 \times 6 + 9 \\ = 69$
69 is the number

Answer 2

let the original no. is 10x+y
where the unit place is y
let the tens place is x
then, according to question
the no is reverse
10y+x
10x+y=15...(1)
10y+x+27
eq.
10x+y=10y+x+27
then I hope you can solve it.