Question

If FI and F2 are the fourth proportional to 2/7 ,7/12,8 and 5/6 , 4/3,10, respectively, then what is F1 : F2?

• A. 16:9
• B. 49:48
• C. 49:16
• D. 25:16

Answer 1

Answer:

B. 49:48

For four numbers (a, b, c, d), if (d) is the fourth proportional, then:

a:b = c:d

So,
$d=\frac{b \times c}{a}$

Finding $(F_1)$

Fourth proportional to:

$\frac{2}{7},\ \frac{7}{12},\ 8$

$F_1=\frac{\frac{7}{12}\times 8}{\frac{2}{7}}$

$=\frac{56}{12}\times\frac{7}{2}$

$=\frac{14}{3}\times\frac{7}{2}$

$=\frac{49}{3}$

Finding $(F_2)$

Fourth proportional to:

$\frac{5}{6},\ \frac{4}{3},\ 10$

$F_2=\frac{\frac{4}{3}\times 10}{\frac{5}{6}}$
$=\frac{40}{3}\times\frac{6}{5}$
=16

Ratio $(F_1 : F_2)$
$\frac{49}{3} : 16$

Multiply both terms by 3:

$49 : 48$

So, the answer is:

$\boxed{49:48}$