If $$\frac{a}{b} = \frac{b}{c} = \frac{c}{d},$$ then $$\frac{{{b^3} + {c^3} + {d^3}}}{{{a^3} + {b^3} + {c^3}}}$$ will be equal to -
A. $$\frac{a}{b}$$
B. $$\frac{b}{c}$$
C. $$\frac{c}{d}$$
D. $$\frac{d}{a}$$
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & {\text{Let }}\frac{a}{b} = \frac{b}{c} = \frac{c}{d} = k \cr & {\text{Then,}} \cr & a = bk, \cr & b = ck, \cr & c = dk \cr & {\text{Also,}} \cr & \Rightarrow \frac{a}{b} \times \frac{b}{c} \times \frac{c}{d} = {k^3} \cr & \Rightarrow {k^3} = \frac{a}{{d}} \cr & \therefore \frac{{{b^3} + {c^3} + {d^3}}}{{{a^3} + {b^3} + {c^3}}} \cr & = \frac{{{b^3} + {c^3} + {d^3}}}{{{{\left( {bk} \right)}^3} + {{\left( {ck} \right)}^3} + {{\left( {dk} \right)}^3}}} \cr & = \frac{{{b^3} + {c^3} + {d^3}}}{{{k^3}\left( {{b^3} + {c^3} + {d^3}} \right)}} \cr & = \frac{1}{{{k^3}}} \cr & = \frac{d}{a} \cr} $$Related Questions on Ratio
If a : b : c = 3 : 4 : 7, then the ratio (a + b + c) : c is equal to
A. 2 : 1
B. 14 : 3
C. 7 : 2
D. 1 : 2
If $$\frac{2}{3}$$ of A=75% of B = 0.6 of C, then A : B : C is
A. 2 : 3 : 3
B. 3 : 4 : 5
C. 4 : 5 : 6
D. 9 : 8 : 10
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