Question

The sum of the digits of two-digit number is 9.  If 27 is subtracted from the number, the digits are reversed. find the number.

Answer 1

Digit in Tens place = x 
Digit in units place = y
The number is 10x + y
Sum of digits = x + y = 9 ....(1)

If 27 is subtracted from the number, the digits are reversed.

10x + y - 27 = 10y + x
⇒ 9x - 9y = 27
⇒ x - y = 3    ........(2)

Solving equations (1) and (2)
 We get, x = 6 and y = 3

the number is 63 

Answer 2

let the two digit no be 10x+y
 given x+y = 9 --------- (1)
 when 27 is subtracted,
 10x+y-27 = 10y+x
 9x-9y-27 = 0
     x-y = 3 ----------- (2)
from (1) & (2)
 x+y = 9
 x--y = 3
-------------
2x = 12
 x = 6
sub x = 6 in (1)
x+y = 9⇒ 6+y = 9
                   y= 3
required no (10x+y) = 10(6)+3
                             = 63