If a fraction is multiplied by itself and then divided by the reciprocal of the same fraction, the result obtained is $$49\frac8{27}$$​ . Find the fraction.

Correct option is A

Given:

A fraction is multiplied by itself and then divided by its reciprocal.

The result is $$49 \frac{8}{27}$$​​

Solution:

Let the fraction be x

Multiplying a fraction by itself:

​$$x \times x = x^2$$​​

Dividing by its reciprocal: 

​$$x^2 \div \left(\frac{1}{x}\right) = x^2 \times x = x^3$$

Now,

​$$x^3 = 49 \frac{8}{27}$$​​

​$$x^3 = \frac{1331}{27}$$​​

​$$x = \frac{\sqrt[3]{1331}}{\sqrt[3]{27}} = \frac{11}{3} = 3 \frac{2}{3}$$​​

Thus, The fraction is (a) $$3 \frac{2}{3}$$