Question

the sum of two digit number and the number obtained by reversing the digit is 165 . if the digits differ by 3 find the number

Answer 1

$let \: the \: two \: digit \: number \: be \: 10x + y. \\ \\ after \: reversing \: the \: number \: \\ becomes \: 10y + x. \\ \\ according \: to \: question \\ 10x + y + 10y + x = 165 \\ 11x + 11y = 165 \\ 11(x + y) = 165 \\ x + y = \frac{165}{11} \\ x + y = 15 \\ x = 15 - y \: \: \: \: \: \: ................(1)$
The digits differ by 3.
Let x>y.
i.e,
$x = y + 3 \: \: \: \: \: \: \: .................(2)$
from eq (1) & (2)

$15 - y = y + 3 \\ 15 - 3= 2y \\ y = \frac{12}{2} \\ y = 6$
from eq (2)
$x = 6 + 3 \\ x = 9$
$so \: the \: digit \: is \: 96 \: or \: 69.$