Question

A number consists of two digits whose sum is 10 .If 8 times the unit digit is added to the number , the digits interchange their places. Find the original no.

Answer 1

Let ten's digit be x and unit place digit be y
$x + y = 10 - - - (1)\\ (10x + y) + 8y = 10y + x \\ 9x = y \\ substituting \: y \: in \: (1) \\ x + 9x = 10 \\ x = 1 \\ therefore \: \: y = 9$
Thus original number is 19