The Difference of Two Natural Numbers is 5 and the Difference of Their Reciprocals is 5/14. Find the Numbers. - Mathematics

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The difference of two natural numbers is 5 and the difference of their reciprocals is 5/14. Find the numbers.

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Let a and b be two natural number such that, a>b


`a−b=5 ...(1)`

`and 1/b−1/a=5/14`



`⇒ab=14 ...(2)`

Putting the value of a from equation (1) in equation (2), we get







⇒b=2 or b=−7

Since, b is natural number, neglecting the value, b = −7,we get

So, the required natural numbers are 7 and 2.

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
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2013-2014 (March) Delhi Set 3

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