Determine if the following are in proportion.(a) 15, 45, 40, 120 (b) 33, 121, 9,96 (c) 24, 28, 36, 48(d) 32, 48, 70, 210 (e) 4, 6, 8, 12 (f) 33, 44, 75, 100.

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To do:

We have to determine whether the given numbers are in proportion.

Solution:

We know that,

The proportion is defined as the equality of two ratios.

If $p,q,r,s$ are in proportion then,

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

(a) The ratio of the first two numbers $=\frac{15}{45}$

$=\frac{1}{3}$

The ratio of the second two numbers $=\frac{40}{120}$

$=\frac{1}{3}$

Since,

$\frac{15}{45} = \frac{1}{3} = \frac{40}{120}$

The given numbers are in proportion.

(b) The ratio of the first two numbers $=\frac{33}{121}$

$=\frac{3}{11}$

The ratio of the second two numbers $=\frac{9}{96}$

$=\frac{3}{32}$

Since,

$\frac{33}{121} ≠ \frac{9}{96}$

The given numbers are not in proportion.

(c) The ratio of the first two numbers $=\frac{24}{28}$

$=\frac{6}{7}$

The ratio of the second two numbers $=\frac{36}{48}$

$=\frac{3}{4}$

Since,

$\frac{24}{28} ≠ \frac{36}{48}$

The given numbers are not in proportion.

(d) The ratio of the first two numbers $=\frac{32}{48}$

$=\frac{2}{3}$

The ratio of the second two numbers $=\frac{70}{210}$

$=\frac{1}{3}$

Since,

$\frac{32}{48} ≠ \frac{70}{210}$

The given numbers are not in proportion.

(e) The ratio of the first two numbers $=\frac{4}{6}$

$=\frac{2}{3}$

The ratio of the second two numbers $=\frac{8}{12}$

$=\frac{2}{3}$

Since,

$\frac{4}{6}=\frac{2}{3}=\frac{8}{12}$

The given numbers are in proportion.

(f) The ratio of the first two numbers $=\frac{33}{44}$

$=\frac{3}{4}$

The ratio of the second two numbers $=\frac{75}{100}$

$=\frac{3}{4}$

Since,

$\frac{33}{44}=\frac{3}{4}=\frac{75}{100}$

The given numbers are in proportion.

Updated on 10-Oct-2022 13:36:49