Question

A number consists of two digits whose sum is 9. If 27 is subtracted from the number, the interchange their place. Find the number.

Answer 1

Let us assume, x and y are the two digits of the two-digit number

Therefore, the two-digit number = 10x + y and reversed number = 10y + x

Given:

x + y = 9 -------------1

also given:

10x + y - 27 = 10y + x
9x - 9y = 27
x - y = 3 --------------2

Adding equation 1 and equation 2

2x = 12
x = 6

Therefore, y = 9 - x = 9 - 6 = 3

The two-digit number = 10x + y = 10*6 + 3 = 63

Answer 2

x+y=9
Number=xy=10x+y
10x+y-27=10y+x
9x-9y=27
x+y=9
9x-9y=27
-9x-9y=-81
-18y=-54
y=3
x+3=9
x=6