Question

The sum of the digits of a 2 digit number is 10 .if we reverse the digits, the new number will be 54 more than the original number .what is original number?

Answer 1

let the no. be x and y
x+y=10 (1)
on reversing no. will be 10y +x
acc. to ques
10y+x= 54+ 10x+y
9y=54+9x
y=6+x (2)
y=10-x (1)

(2)-(1)

0=-4+2x
x=2
and
y=8

Answer 2

let the digit of the nos are x (oneplaced) and y(10placed)
so the no is 10y+x
if the digits are reversed
then the no is 10x+y
so by question 10x+y=54+10y+x
or 9x-9y=54
or x-y=6..... (1)
and x+y=10...... (2) given
so 2x=16
or x=8
y =2
so the original no is 10y+x=10*2+8=28