If (m + n) : (m – n) = 7 : 3, then $$(\text{m}^3+\text{n}^3) : (\text{m}^3-\text{n}^3)$$​ = ?

Correct option is B

Given:
The ratio (m + n) : (m - n) = 7 : 3
Concept Used:
Ratios and Proportions:
If $$\frac{a}{b} = \frac{c}{d}$$​, then by Componendo and Dividendo, we have $$\frac{a + b}{a - b} = \frac{c + d}{c - d}$$​

Solution:

​$$\frac{m + n}{m - n} = \frac{7}{3}$$​

​$$\frac{(m + n) + (m - n)}{(m + n) - (m - n)} = \frac{7 + 3}{7 - 3}$$​

​$$\frac{2m}{2n} = \frac{10}{4}$$​

​$$\frac{m}{n} = \frac{5}{2}$$​​
Let m = 5k and n = 2k (where k is a constant).
Using m = 5k and n = 2k:
​$$m^3 + n^3 = (5k)^3 + (2k)^3 = 125k^3 + 8k^3 = 133k^3$$​​
​$$m^3 - n^3 = (5k)^3 - (2k)^3 = 125k^3 - 8k^3 = 117k^3$$​​
​$$\frac{m^3 + n^3}{m^3 - n^3} = \frac{133k^3}{117k^3} = \frac{133}{117}$$​​