The sum of a two digit number and the number obtained by interchanging the digits of the number is 121. If the digits of the number differ by 3, find the number.
Linear Equations
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Question

The sum of a two digit number and the number obtained by interchanging the digits of the number is 121. If the digits of the number differ by 3, find the number.

KnowledgeBoat · Accepted Answer

Let x be the digit at ten's place and y be the digit at unit's place. Number = 10(x) + y = 10x + y On reversing digits, the number becomes = 10(y) + x = 10y + x. Given, The sum of a two digit number and the number obtained by interchanging the digits of the number is 121. ∴ 10x + y + 10y + x = 121 ⇒ 11x + 11y = 121 ⇒ 11(x + y) = 121 ⇒ x + y = 11 ..........(1) Let digits of the number differ by 3. ⇒ x - y = 3 ........(2) or ⇒ y - x = 3..........(3) Considering x - y = 3, Adding equation (1) and (2), we get : ⇒ x + y + x - y = 11 + 3 ⇒ 2x = 14 ⇒ x = 7. Substituting value of x in equation (1), we get : ⇒ 7 + y = 11 ⇒ y = 11 - 7 ⇒ y = 4. Number = 10x + y = 10(7) + 4 = 70 + 4 = 74. Considering y - x = 3, Adding equation (1) and (3), we get : ⇒ x + y + y - x = 11 + 3 ⇒ 2y = 14 ⇒ y = ⇒ y = 7. Substituting value of x in equation (1), we get : ⇒ x + 7 = 11 ⇒ x = 11 - 7 ⇒ x = 4. Number = 10x + y = 10(4) + 7 = 40 + 7 = 47. Hence, number = 47 or 74.

Mathematics

The sum of a two digit number and the number obtained by interchanging the digits of the number is 121. If the digits of the number differ by 3, find the number.

Linear Equations

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