# Aptitude Question ID : 93605

If b is the mean proportional of a and c, then $(a-b)^{3} : (b-c)^{3}$ is equal to:
[A]$a^{3}:b^{3}$
[B]$a^{2}:c^{2}$
[C]$b^{2}:c^{2}$
[D]$a^{3}:c^{3}$

$\mathbf{a^{3}:b^{3}}$
Since b is the mean proportional of a and c.
$\therefore \frac{a}{b} = \frac{b}{c} = k(suppose)$
$\therefore a = bk, b=ck$
$\therefore \frac{(a-b)^{3}}{(b-c)^{3}} = \frac{(bk-b)^{3}}{(ck-c)^{3}}$
$= \frac{b^{3}(k-1)^{3}}{c^{3}(k-1)^{3}} = \frac{b^{3}}{c^{3}} = \frac{a^{3}}{b^{3}} = a^{3} : b^{3}$
Hence option [A] is the right answer.