The fourth proportional of a, c and bc is d. The fourth proportional of bc²/a, ad/c and c is ______.

Correct option is B

Given:

The fourth proportional of a, c, and bc is d.

We need to find the fourth proportional of $$\frac{bc^2}{a}, \frac{ad}{c}, c.$$​​

Formula Used:

The fourth proportional x is:

x = $$\frac{b_1 \times c_1}{a_1}$$​​

Solution:

Using the formula for the fourth proportional:

d = $$\frac{c \times bc}{a} = \frac{bc^2}{a}$$​​

Now,

Let:

A = $$\frac{bc^2}{a}$$​, B = $$\frac{ad}{c}$$​ , C = c

Using the formula for the fourth proportional:

Fourth proportional = $$\frac{\left(\frac{ad}{c}\right) \times c}{\frac{bc^2}{a}}$$​​

​$$= \frac{ad}{\frac{bc^2}{a}} = ad \times \frac{a}{bc^2}$$​​

​$$= \frac{a^2d}{bc^2}$$​​

Substituting the value of d:

= $$\frac{a^2 \times \frac{bc^2}{a}}{bc^2}$$​​

​$$= \frac{a \times bc^2}{bc^2} = a$$​​

Thus, the fourth proportional of  $$\frac{bc^2}{a}, \frac{ad}{c}, c$$ is a