Four times a certain two digit number is seven times the number obtained on interchanging its digits. If the difference between the digits is 4; find the number.
Linear Equations
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Question

Four times a certain two digit number is seven times the number obtained on interchanging its digits. If the difference between the digits is 4; 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, Difference between digits = 4 ⇒ x - y = 4 ⇒ x = y + 4 .....(1) Given, Four times a certain two digit number is seven times the number obtained on interchanging its digits. ⇒ 4(10x + y) = 7(10y + x) ⇒ 40x + 4y = 70y + 7x ⇒ 40x - 7x = 70y - 4y ⇒ 33x = 66y ⇒ x = ⇒ x = 2y .........(2) From (1) and (2), we get : ⇒ 2y = y + 4 ⇒ 2y - y = 4 ⇒ y = 4 Substituting value of y in equation (1), we get : ⇒ x = y + 4 = 4 + 4 = 8. Number = 10x + y = 10(8) + 4 = 80 + 4 = 84. Hence, number = 84.

Mathematics

Four times a certain two digit number is seven times the number obtained on interchanging its digits. If the difference between the digits is 4; find the number.

Linear Equations

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