Aptitude Question ID : 93605

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

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


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