Question

The sum of the digits of a two - digit numbers is 9. if 45 is added to the number the digits get reversed find the number

Answer 1

Let the unit digit be x
and ten's digit be y

Original number :- 10y + x

as given that the sum of the digit is 9

then,

x + y = 9

x = 9 - y ..... ( i )


Now ,

if 45 is added the number gets reversed

so ,

10y + x + 45 = 10x + y

10y - y + x - 10x + 45 = 0

9y - 9x + 45 = 0

y - x + 5 = 0 ...... ( ii )


Putting the value of x from ( i ) in ( ii )


y - x + 5 = 0

y - ( 9 - y ) + 5 = 0

y - 9 + y + 5 = 0

2y - 4 = 0

y = 4/2

y = 2


Putting the value of y in ( i )

x = 9 - y

x = 9 - 2

x = 7


So,

the required number is :-

10y + x

10 × 2 + 7

20 + 7

27


27 is the required two digit number!