If a : b = c : d = e : f = 2 : 3, then (xa + yc +ze) : (xb + yd + zf) = __________.

Correct option is B

Given:

a : b = c : d = e : f = 2 : 3
Solution:
Given the relations $$\frac{a}{b} = \frac{2}{3}, \frac{c}{d} = \frac{2}{3}, and \frac{e}{f} = \frac{2}{3},$$​​
a = $$\frac{2}{3}b, \quad c = \frac{2}{3}d, \quad e = \frac{2}{3}f$$​​
Now, substitute these expressions into the given ratio:
​$$\frac{xa + yc + ze}{xb + yd + zf} = \frac{x \times \frac{2}{3}b + y \times \frac{2}{3}d + z \times \frac{2}{3}f}{x \times b + y \times d + z \times f}$$​​

= $$\frac{\frac{2}{3} (xb + yd + zf)}{xb + yd + zf}$$​​
= $$\frac{2}{3}$$​​
So, the ratio is 2 : 3.

Thus the correct option is(b) 2:3