Question

A number consists of two digits whose sum is 8. if 18 is subtracted from the number the digits interchange their places . what is the number.

Answer 1

Let the unit digit be x
and tens digit be y


The original number :- 10y + x


• Sum of digit is 8

x + y = 8

x = 8 - y .....( i )


• 18 is subtracted from the number the digit interchange their places.

10y + x - 18 = 10x + y

10y - y + x - 10x = 18

9y - 9x = 18

( dividing by 9 )

y - x = 18 ....( ii )

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

y - x = 18

y - ( 8 - y ) = 18

y - 8 + y = 18


2y = 18 - 8

2y = 10

y = 5


Putting the value of y in ( i )

x = 8 - y

x = 8 - 5

x = 3



The required number is

10y + x

10 × 5 + 3

50 + 3

53