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 143. Find both the numbers.

Let the digit at the tens place be x and the digit at the units place be y.

Then the original two-digit number = 10x + y.

When the digits are interchanged, the new number = 10y + x.

According to the question, the digits differ by 3.

So, |x - y| = 3

This gives us either x - y = 3 or y - x = 3.

Also, the sum of the original number and the interchanged number is 143.

So,

(10x + y) + (10y + x) = 143

⇒ 11x + 11y = 143

⇒ 11(x + y) = 143

⇒ x + y = $\dfrac{143}{11}$

⇒ x + y = 13

Case 1: x - y = 3

Adding x + y = 13 and x - y = 3:

2x = 16

⇒ x = 8

Substituting x = 8 in x + y = 13:

8 + y = 13

⇒ y = 5

Original number = 10(8) + 5 = 85

Interchanged number = 10(5) + 8 = 58

Case 2: y - x = 3

Adding x + y = 13 and y - x = 3:

2y = 16

⇒ y = 8

Substituting y = 8 in x + y = 13:

x + 8 = 13

⇒ x = 5

Original number = 10(5) + 8 = 58

Interchanged number = 10(8) + 5 = 85

Hence, the two numbers are 58 and 85.