Question

a number consists of two digits whose sum is 9 if 27 is subtracted from the number its digits are reversed find the number

Answer 1

Let the number be xy.

Therefore x+y = 9…(1)

10x+y-27 = 10y+x

9x-9y=27

9(x-y)=27

x-y = 3…(2)

That means, by adding 1 and 2, we get:

2x=12

x=6

y = 3

Number is 63

Answer 2

Let us assume, a and b are the two digits of the two-digit number

Therefore, the two-digit number = 10a + yb and reversed number = 10b + a

Given:

a + b = 9 -------------1

also given:

10a + b - 27 = 10b + a

9a - 9b = 27

a - b = 3 --------------2

Adding equation 1 and equation 2

2a = 12

a = 6

Therefore, b = 9 - a = 9 - 6 = 3

The two-digit number = 10a + b = 10*6 + 3 = 63