Question

The sum of a two-digit number and the number obtained by reversing the order of its digits is 121, and the two digits differ by 3. Find the number.

Answer 1

Let x be the ones digit and y be the tens digit. Then

Two digit number before reversing = 10y + x

Two digit number after reversing = 10x + y

As per the question

(10y + x) + (10x + y) = 121

⇒ 11x + 11y = 121

⇒ x + y = 11          ...(i)

Since the digits differ by 3, so

x – y = 3          ...(ii)

Adding (i) and (ii), we get

2x = 14

⇒ x = 7

Putting x = 7 in (i), we get

7 + y = 11

⇒ y = 4

Changing the role of x and y, x = 4 and y = 7

Hence, the two-digit number is 74 or 47.