Write True ( T ) or False ( F ) against each of the following statements :
(a) 16 : 24 :: 20 : 30
(b) 21: 6 :: 35 : 10
(c) 12 : 18 :: 28 : 12
(d) 8 : 9 :: 24 : 27
(e) 5.2 : 3.9 :: 3 : 4
(f) 0.9 : 0.36 :: 10 : 4.

To do:

We have to write True ( T ) or False ( F ) against each of the given statements.

Solution:

We know that,

The proportion is defined as the equality of two ratios.

If $p:q::r:s$ then, 

$\frac{p}{q} = \frac{r}{s}$.

(a) 16:24:: 20:30

$16:24 = \frac{16}{24}$

$=\frac{2}{3}$

$20:30 = \frac{20}{30}$

$=\frac{2}{3}$

Since,

$16:24 = 20:30$

The given statement is True.

(b)  21: 6:: 35: 10

$21:6 = \frac{21}{6}$

$=\frac{7}{2}$

$35:10 = \frac{35}{10}$

$=\frac{7}{2}$

Since,

$21:6 = 35:10$

The given statement is True.

(c) 12 : 18 :: 28 : 12

$12:18 = \frac{12}{18}$

$=\frac{2}{3}$

$28:12 = \frac{28}{12}$

$=\frac{7}{3}$

Since,

$12:18 ≠ 28:12$

The given statement is False.

(d) 8 : 9:: 24: 27

$8 : 9 = \frac{8}{9}$

$24 : 27 = \frac{24}{27}$

$=\frac{8}{9}$

Since,

$8 : 9= 24 : 27$

The given statement is True.

(e)  5.2: 3.9:: 3: 4

$5.2 : 3.9 = \frac{5.2}{3.9}$

$=\frac{52}{39}$

$=\frac{4}{3}$

$3 : 4 =\frac{3}{4}

Since,

$5.2: 3.9 ≠ 3:4$

 The given statement is False.

(f) 0.9 : 0.36 :: 10 : 4

$0.9 : 0.36 =\frac{0.9}{0.36}$

$=\frac{90}{36}$

$=\frac{10}{4}$

$10 : 4 = \frac{10}{4}$

Since,

$0.9 : 0.36 = 10 :4$

The given statement is True.

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Updated on: 10-Oct-2022

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