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.
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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.

KnowledgeBoat · Accepted Answer

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 = ⇒ 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.

Mathematics

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.

Polynomials

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