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Question

Divide 77 into two parts such that the sum of their reciprocals is \(\frac{7}{12} \). From which of the following equations, we can get the required numbers? (Take one required number as x).

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Solution

Let one number be x. Then, the other number will be 77-x.

Reciprocals of the given numbers are :

\(\frac {1}{x} \) and \(\frac {1}{77-x} \)

It is given that sum of their reciprocals is \(\frac{7}{12} \)

\(\Rightarrow \frac {1}{x} + \frac {1}{77-x} =\frac{7}{12}\)


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