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.

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