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  1. If b is the mean proportional of a and c, then (a – b)3 : (b – c)3 equals
    1. a3 : c3
    2. b2 : c2
    3. a2 : c2
    4. a3 : b3
Correct Option: D

Since b is the mean proportional of a and c.

∴ 
a
 =
b
 = k (Suppose)
bc

∴  a = bk, b = ck
∴ 
(a − b)3
 =
(bk − b)3
(b − c)3(ck − c)3

=
b3(k − 1 )3
 =
b3
 =
a3
c3(k − 1 )3c3b3


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