A two-digit number is such that the ten's digit exceeds twice the unit's digit by 2 and the number obtained by inter-changing the digits is 5 more than three times the sum of the digits. Find the two digit number.
Linear Equations
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Question

A two-digit number is such that the ten's digit exceeds twice the unit's digit by 2 and the number obtained by inter-changing the digits is 5 more than three times the sum of the digits. Find the two digit number.

Linear Equations

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KnowledgeBoat · Accepted Answer

Let x be the digit at ten's place and y be the digit at unit's place. Given, Ten's digit exceeds twice the unit's digit by 2. ∴ x - 2y = 2 ⇒ x = 2y + 2 ........(1) Given, Number obtained by inter-changing the digits is 5 more than three times the sum of the digits. ∴ 10y + x = 3(x + y) + 5 ⇒ 10y + x = 3x + 3y + 5 ⇒ 10y - 3y + x - 3x = 5 ⇒ 7y - 2x = 5 ........(2) Substituting value of x from equation (1) in equation (2), we get : ⇒ 7y - 2(2y + 2) = 5 ⇒ 7y - 4y - 4 = 5 ⇒ 3y - 4 = 5 ⇒ 3y = 9 ⇒ y = = 3. Substituting value of y in equation (1), we get : ⇒ x = 2y + 2 = 2(3) + 2 = 6 + 2 = 8. Original number = 10x + y = 10(8) + 3 = 80 + 3 = 83. Hence, original number = 83.

Mathematics

A two-digit number is such that the ten's digit exceeds twice the unit's digit by 2 and the number obtained by inter-changing the digits is 5 more than three times the sum of the digits. Find the two digit number.

Linear Equations

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