Question

The sum of the digits of a 2-digit number is 13. When 27 is subtracted from it, the digits get reversed. Find the number.

Options

• 94

• 49

• 58

• 85

Answer 1

85

Explanation:

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

x = tens digit,

y = units digit,

Given:

x + y = 13     ...(1)

10x + y − 27 = 10y + x

(10x − x) + (y − 10y) = 27

9x − 9y = 27    ...(Dividing equation by 9)

x − y = 3     ...(2)

Now adding equation (1) and equation (2):

(x + y) + (x − y) = 13 + 3

2x = 16

x = `16/2`

∴ x = 8

Substitute x = 8 in equation (1):

8 + y = 13

y = 13 − 8

∴ y = 5

Hence, the number is 10x + y,

= 10(8) + 5

= 80 + 5

= 85