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If we multiply a fraction by itself and divide the product by its reciprocal, the fraction thus obtained is $15 \frac{5}{8}.$ The original fraction is :

1. $2 \frac{1}{2}$
2. $3 \frac{1}{2}$
3. $\frac{8}{125}$
4. $\frac{125}{8}$

Let the fraction is $p/q$ and it’s reciprocal is $q/p$. now according to the question:

$\implies\frac{\frac{p}{q}\times\frac{p}{q}}{\frac{q}{p}}=\frac{125}{8}$

$\implies \left ( \frac{p}{q} \right )^3=\frac{125}{8}$

$\implies \left ( \frac{p}{q} \right )=\frac{5}{2}=2 \frac{1}{2}$

Option (A) is correct.
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