Question

Qn 8 . The sum of digit of two digit number is 1 by 8 of the number if the digit are reversed the new number is 45 less than the original number find the original number

Answer 1

let the ones digit number = x 
similarly tens digit number = y 
Original number = x + 10y 

ATQ 
x +y = 1/8(x + 10y) 

8x + 8y = x + 10y 

7x = 2y ---(1)

x = 2y/7 ---(2) 

also ...

10x + y = 10y+x - 45 

9x = 9y - 45 ---(3)

x = 9y-45/9 ---(4)

by 3 and 4 

2y/7 = 9y-45/9 

18y = 63y - 315 

315 = 63y - 18y 

315 = 45y 

y = 315/45
y = 7 

similarly x = 2 x 7 /7 = 2 

original number = 10 x 7 + 2 

=72