Seven times a two digit number is equal to four times the number obtained by reversing the digits. If the difference between the digits is 3, find the number.
Linear Equations
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Seven times a two digit number is equal to four times the number obtained by reversing the digits. If the difference between the digits is 3, find the number.

KnowledgeBoat · Accepted Answer

Let digit at ten's place be x and digit at unit's place be y. Number = 10(x) + y = 10x + y On reversing the digits, Reversed number = 10(y) + x = 10y + x Given, Seven times a two digit number is equal to four times the number obtained by reversing the digits. ⇒ 7(10x + y) = 4(10y + x) ⇒ 70x + 7y = 40y + 4x ⇒ 40y - 7y = 70x - 4x ⇒ 33y = 66x ⇒ y = ⇒ y = 2x ..........(1) Given, Difference between the digits is 3. Let x y ⇒ x - y = 3 ..........(2) Let y x ⇒ y - x = 3 ..........(3) Substituting value of y from equation (1) in equation (2), we get : ⇒ x - 2x = 3 ⇒ -x = 3 ⇒ x = -3 This is not possible as digits cannot be negative. Substituting value of y from equation (1) in equation (3), we get : ⇒ 2x - x = 3 ⇒ x = 3 Substituting value of x in equation (1), we get : ⇒ y = 2x = 2(3) = 6. Number = 10x + y = 10(3) + 6 = 30 + 6 = 36. Hence, number = 36.

Mathematics

Seven times a two digit number is equal to four times the number obtained by reversing the digits. If the difference between the digits is 3, find the number.

Linear Equations

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