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 the result is 143. Find the original number.

Let the original number be 10x + y.

As it is given that, the digits of a two-digit number differ by 3.

⇒ x - y = 3

⇒ x = 3 + y ……………(1)

If the digits are interchanged, the new number is 10y + x

The sum of interchanged number and original number is 143.

⇒ (10y + x) + (10x + y) = 143

⇒ 10y + x + 10x + y = 143

⇒ 11y + 11x = 143

⇒ 11(y + x) = 143

⇒ y + x = $\dfrac{143}{11}$

⇒ y + x = 13

From equation (1),

⇒ y + (3 + y) = 13

⇒ y + 3 + y = 13

⇒ 2y + 3 = 13

⇒ 2y = 13 - 3

⇒ 2y = 10

⇒ y = $\dfrac{10}{2}$

⇒ y = 5

x = y + 3

x = 5 + 3

x = 8

Original number = 10x + y

= 10 $\times$ 8 + 5

= 80 + 5

= 85

Hence, the original number is 85.