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?

SSC GD Constable 5 Feb 2025 Shift 2 Paper

Section: Elementary Mathematics

Question : 52 of 80

Marks: +1, -0

If F1 and F2 are the fourth proportional to

\;{2}/{7},\;{7}/{12},8

and

\;{5}/{6},\;{4}/{3},10

, respectively, then what is F1 : F2?

Solution:

a, b, c

are given, and d is the fourth proportional, then:

\;d=(b × c) \/ a

\;F_1: F_2=F_1 \/ F_2

Calculation:
For

F _1

a=2 \/ 7, b=7 \/ 12, c=8

Using the formula,

\;⇒ F_1=(b × c) \/ a

\;⇒ F_1=((7 \/ 12) × 8) \/(2 \/ 7)

\;⇒ F_1=(56 \/ 12) ÷(2 \/ 7)

\;⇒ F_1=(56 \/ 12) ×(7 \/ 2)

\;⇒ F_1=(56 × 7) \/(12 × 2)

\;⇒ F_1=392 \/ 24

\;⇒ F_1=49 \/ 3

For

F _2

a=5 \/ 6, b=4 \/ 3, c=10

Using the formula,

\;⇒ F_2=(b × c) \/ a

\;⇒ F_2=((4 \/ 3) × 10) \/(5 \/ 6)

\;⇒ F_2=(40 \/ 3) ÷(5 \/ 6)

\;⇒ F_2=(40 \/ 3) ×(6 \/ 5)

\;⇒ F_2=(40 × 6) \/(3 × 5)

\;⇒ F_2=240 \/ 15

\;⇒ F_2=16

Now,

F _1: F _2= F _1 \/ F _2

\;⇒ F_1: F_2=(49 \/ 3) ÷ 16

\;⇒ F_1: F_2=(49 \/ 3) ×(1 \/ 16)

\;⇒ F_1: F_2=49 \/ 48

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