Question

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​

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