The sum of the digits of a two-digit number is 7 . The number obtained by interchanging the digits exceeds the original number by 27 . Find the number.

Question

This is question from 8th class book chapter Linear Equations

Answer 1

Let  xy be a two-digit number such that

x+y=7

yx=xy+27

 

x+y=7

10y+x=10x+y+27

x+y=7

-9x+9y=27

 

x+y=7

x-y=-3

x=2

y=5

 

The number is 25. 

xy+27=yx

25+27=52