If $$a,b,c$$​ and $$d$$​ are in continued proportion, then $$(ma^3+nb^3-rc^3):(mb^3+nc^3-rd^3)$$​ = ?

Correct option is B

Given:

a, b, c, d are in continued proportion.

​$$(ma^3 + nb^3 - rc^3) : (mb^3 + nc^3 - rd^3)$$ = ?

Solution:​

​$$\frac ab = \frac bc =\frac cd = k$$​​

a = bk ....(1)

b = ck  ....(2)

c = dk   ....(3)

Solving above equation,

abc = $$k^3$$ bcd

$$k^3$$ = $$\frac{abc}{bcd}$$   ....(4)

Now,

$$\frac{mb^3k^3+ nc^3k^3-rd^3k^3}{mb^3+nc^3-rd^3}$$

=$$\frac{k^3(mb^3+ nc^3-rd^3)}{mb^3+nc^3-rd^3}$$ 

Using equation (4) , we have-

=$$k^3$$ = $$\frac{abc}{bcd}$$ = $$\frac ad$$​