Question

The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is ______.

Options

• 27

• 72

• 45

• 36

Answer 1

The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is 36.

Explanation:

Let the original two-digit number be 10x + y, where:

x is the tens digit,

y is the units digit,

Given: x + y = 9     ...(1)

Adding 27 reverses the digits:

10x + y + 27 = 10y + x

(10x − x) + (y − 10y) = −27

9x − 9y = −27

x − y = −3     ...(2)

Now adding equations (1) and (2):

(x + y) + (x − y) = 9 + (−3)

2x = 6

x = `6/2`

∴ x = 3

Substitute x = 3 in equation (1):

3 + y = 9

y = 9 − 3

∴ y = 6

So the number is 10x + y,

= 10(3) + 6

= 30 + 6

= 36