Question : The reciprocal of the sum of the reciprocals of $\frac{2}{9}$ and $\frac{7}{10}$ is:
Option 1: $\frac{14}{83}$
Option 2: $\frac{83}{14}$
Option 3: $\frac{90}{83}$
Option 4: $\frac{83}{90}$
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Correct Answer: $\frac{14}{83}$
Solution :
Reciprocal of $\frac{2}{9}=\frac{9}{2}$
Reciprocal of $\frac{7}{10}=\frac{10}{7}$
Their sum = $(\frac{9}{2}+\frac{10}{7})=(\frac{63+20}{14} )=(\frac{83}{14} )$
$\therefore$ Reciprocal of the Sum = $\frac{14}{83}$
Hence, the correct answer is $\frac{14}{83}$.
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