NIELIT 2022 Feb Scientist D - Section D: 5

Question

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 :

• A. $2 \frac{1}{2}$
• B. $3 \frac{1}{2}$
• C. $\frac{8}{125}$
• D. $\frac{125}{8}$

Answer 1

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.