If F1 and F2 are the fourth proportional to $$\frac{2}{7}, \frac{7}{12}$$, 8  and $$\frac{5}{6}, \frac{4}{3}$$, 10 respectively, then what is F1 : F2?

Correct option is B

Given:

F₁ and F₂ are the fourth proportional to$$\frac{2}{7} : \frac{7}{12} : 8$$​ and $$\frac{5}{6} : \frac{4}{3} : 10$$​, respectively.

Formula Used:
For two ratios $$\frac{a}{b}, \frac{c}{d}$$​ and x, y, if x and y are the fourth proportional, then the relationship is:

​$$\frac{a}{b} = \frac{c}{d} = \frac{x}{y}$$​​

Solution:

For the first ratio:

​$$F_1 = \frac{7 \times7\times 8}{2 \times 12} = \frac{49}{3}$$​​

For the second ratio:

​$$F_2 = \frac{6 \times4\times 10}{5 \times 3} = \frac{60}{15} = {16}$$​​

Now,

​$$F_1 : F_2 = \frac{49}{3} : 16 = \frac{49}{3 \times 16} = \frac{49}{48}$$​​