Question

The digits of a two-digit number differ by 3. If the digits are interchanged and the resulting number is added to the original number, we get 99.what can be the original number? ​

Answer 1

Given :

• The digits of a two-digit number differ by 3.

• The digits are interchanged and the resulting number is added to the original number, we get 99.

To find :

• The Original number =?

Step-by-step explanation:

Let us assume, the x is the tenth place digit and y is the unit place digit of the two-digit number.

Also assume x > y

Therefore, the two-digit number be 10x + y

And, Reversed number be 10y + x

Given:

x - y = 3 .... (1)

Also given:

10x + y + 10y + x = 99

11x + 11y = 99

11 (x + y) = 99

x + y = 99/11

x + y = 9 .... (2)

Adding equation (1) and equation (2).

x - y + x + y = 3 + 9

2x = 12

x = 12/2

x = 6

Therefore, y = x - 3 = 6 - 3 = 3

Thus, the two-digit number = 10x + y = 10 × 6 + 3 = 63

Therefore, The Original number = 63