Question

A number consists of two digits. the sum of digits is 9. if 63 is subtracted from the number, its digits are interchanged. find the number.

Answer 1

Let x and y be the digits
x+y=9 ------(1)
10x+y-63=10y+x
9x-9y=63
Dividing by 9
x-y=7 -------(2)
Now (1) + (2)
x+y=9
x-y=7
----------
2x=16
x=8
Now substituting x=8 in (1)
8+y=9
y=1
Thus the number is 81

Answer 2

Let the ten's digit be x. Then, unit's digit = (9 - x).

Number = l0x + (9 - x) = 9x + 9.

Number obtained by reversing the digits = 10 (9 - x) + x = 90 - 9x.

therefore, (9x + 9) - 63 = 90 - 9x    

=>18x = 144   

=>x = 8.

            So, ten's digit = 8 and unit's digit = 1.
            Hence, the required number is 81.