Question

a number consists of two digits.if the digits interchange their places and the new number is added to the original number then the number becomes two times of the original number.find the number

Answer 1

Suppose x is the digit at the ten's place and y is at the unit's place of the given number
the the given number 10x+y
and if we reverse the order of the digits, the new number becomes 10y+x
then according to the problem
(10x+y)+(10y+x)= 2(10x+y).......(1)

11x+11y=20x+2y
11x+9y=20x
9y=9x
x=y.....(2)
from 1 and 2
2(10x+x)=22x
22x=22x
x=1=y
thus given number is 11
11+11=22
:-)