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.

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.

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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

Related Questions

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