The sum of the digits of a 2 - digit number is 7. If 9 is added to the number, the digits interchange their places. Find the digit at the ten's place of the original number.

3

Let digit at ones place = x

digit at tens place = y

So, Number is 10y + x

ATQ,

x + y = 7    ----(1)

when digits interchange their places ,

10x + y

ATQ,

( 10y + x ) + 9 = 10x + y

9x - 9y = 9

x - y = 1      -----(2)

On adding equation 1 and 2 ,

2x = 7 + 1 = 8

x = 4

So, Digit at tens place is y = 7 - 4 = 3

The correct answer is Option (2) → 3