Question

The digits of a two digit number differ by $7$. If the digits are interchanged and the resulting numbers is added to original numbers, we get $121$. What is the original number?

Answer 1

Given x and y be the required two digit number.

Let the digit in ten's place be x.

Let the digit in one's place be y.

Therefore the required number is 10x+y. ------ (*)

Given that the digits of a two digit number differ by 7.

x - y = 7 ----- (1)

Given that if the digits are interchanged and the resulting number is added to the original number we get 121.

10x + y + 10y + x = 121

11x + 11y = 121

x + y = 11 -------------- (2).

On solving (1) & (2), we get

x + y = 11

x - y = 7

--------------

2x = 18

x = 9

Substitute x = 9 in (1), we get

x + y = 11

9 + y = 11

y = 11 - 9

y = 2.

Substitute x & y in (*), we get

The original number = 10(9) + 2

= 90 + 2

= 92.