The sum of the digits of a two digit number is 7. If the digits are reversed, the new number decreased by 2, equals twice the original number. Find the number.
Linear Equations
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Question

The sum of the digits of a two digit number is 7. If the digits are reversed, the new number decreased by 2, equals twice the original number. Find the number.

KnowledgeBoat · Accepted Answer

Let digit at unit's place be x and ten's place be y. Number = 10 × y + x = 10y + x Given, Sum of digits = 7 ∴ x + y = 7 ⇒ x = 7 - y ........(1) On reversing digits, New number = 10 × x + y = 10x + y Given, The new number decreased by 2, equals twice the original number. ⇒ (10x + y) - 2 = 2(10y + x) ⇒ 10x + y - 2 = 20y + 2x ⇒ 10x - 2x = 20y - y + 2 ⇒ 8x = 19y + 2 ⇒ 8(7 - y) = 19y + 2 ........[From (1)] ⇒ 56 - 8y = 19y + 2 ⇒ 56 - 2 = 19y + 8y ⇒ 54 = 27y ⇒ y = = 2. Substituting value of y in (1), we get : ⇒ x = 7 - 2 = 5. Number = 10y + x = 10 × 2 + 5 = 25. Hence, number = 25.

Mathematics

The sum of the digits of a two digit number is 7. If the digits are reversed, the new number decreased by 2, equals twice the original number. Find the number.

Linear Equations

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