Question

27

Answer 1

Answer:

The original nimber is 67.

Step-by-step explanation:

Let the two digits be x and y.

According to the question.

The sum of two digits of a two digit number is

x + y = 13

or, x = 13 - y

And, a two digit number can be written as

x × 10 + y

when the digits are reversed, the number can be written as

y × 10 + x

the original number increases by 9. i.e.

y x 10 + x = x × 10 + y + 9

Replacing value of x by 13 - y,

y × 10 + 13 - y = 10(13 - y) + y + 9

10y + 13 - y = 130 - 10y + y + 9

9y + 13 = 139 - 9y

18y = 139 - 13

18y = 126

y = 126/18

y = 7

So, x = 13 - y

= 13 - 7

= 6

The original number is x × 10 + y = 6 x 10 + 7 = 67.