A ratio obtained by multiplying or dividing the numerator and the denominator of a given ratio by the same number is called an equivalent ratio.
Hence, when the numerator and the denominator of the given ratio 3 : 2 are multiplied by 4, we get
$\frac{3\times 4}{2\times 4}$ = $\frac{12}{8}=12:8$
$\therefore$ 3 : 2 and 12 : 8 are equivalent ratios.

Weight of 80 identical books = 400 kg
Weight of 1 such book
$=\frac{400}{80}=\frac{10\times 40}{10\times 8}=\frac{40}{8}=5kg$

Ratios are in proportion if they are equal or equivalent. This can be verified by using the product of means and product of extremes.

In a: b :: c: d; 'b' and 'c' are means and 'a' and 'd' are extremes.

For 4 kg : 20 kg :: ₹ 50 : ₹ 250

Product of means = 20 $\times$ 50 = 1000
Product of extremes = 4 $\times$ 250 = 1000
So, this is in proportion.

For 2 dozens : 3 dozens :: ₹ 40 : ₹ 80

Product of means = 3 $\times$ 40 = 120
Product of extremes = 2 $\times$ 80 = 160

So, this is not in proportion.

For  8 liters : 15 liters :: ₹ 25 : ₹ 50
Product of means = 15 $\times$ 25 = 375
Product of extremes = 8 $\times$ 50 = 400

So, this is also not in in proportion.

For  2 km : 3 km :: 1 m : 2m
Product of means = 3 $\times$ 1 = 3
Product of extremes = 2 $\times$ 2 = 4

So, this is also not in in proportion.

Two ratios are said to be in proportion if they are equivalent or equal.
Consider 3:5 :: 12:20
$12:20=\frac{12}{20}=\frac{3}{5}=3:5$
Hence, they are in proportion
Consider 1:2::3:6
$3:6=\frac{3}{6}=\frac{1}{2}=1:2$
Hence, they are in proportion.
Note that 2: 3 and 4: 9 are not in proportion as the product of extremes (2 $\times$ 9 = 18) is not equal to product of means (3  $\times$ 4 = 12).
Similarly, 1:2 and 4:5 are not in proportion as the product of extremes (1 $\times$ 5 = 5) is not equal to product of means (2  $\times$ 4 = 8).

To decrease a quantity in the given ratio a : b, we multiply the given
$\text{quantity by}\frac{b}{a}$, 
where b < a.

Hence, new quantity
= $1551\times \frac{7}{11}$
= $141\times 7$
= $987$

Steps: 1 Mark
Solution: 1 Mark
$\text{Length}\left(l\right):\text{Breadth (b)}=4:5$
$\Rightarrow \frac{l}{b}=\frac{4}{5}$
Given: $l=20m$
$\Rightarrow \frac{20}{b}=\frac{4}{5}$
$\Rightarrow \frac{b}{20}=\frac{5}{4}$
$\Rightarrow b=\frac{5\times 20}{4}$
$b=5\times 5=25$
$\therefore \text{Breadth of the field}=25m$

Steps: 1 Mark
Answer: 1 Mark
If $x:4and6:8$ are equivalent ratios. Then
$x:4=6:8\Rightarrow \frac{x}{4}=\frac{6}{8}$
$\Rightarrow x=\frac{6\times 4}{8}=3$
$\therefore x=3$

Each Option: 1.5 Mark
Number of students liking tennis $=30-(6+12)=30-18=12$
a) Ratio of number of students liking football to number of students liking tennis
 $=6:12=1:2$

b) Ratio of number of students liking cricket to total number of students
 $=12:30=2:5$

Hence,
Ratio of number of students liking football to number of students liking tennis $=1:2$
Ratio of number of students liking cricket to total number of students $=2:5$

Each option: 1 Mark
Total number of students in class$=20+15=35$
(a) Ratio of number of boys to the number of girls
 $=15:20=\frac{15}{20}=\frac{3}{4}$
 Hence, ratio of number of boys to the number of girls is $3:4$
(b) Ratio of number of girls to the total number of students
 $=20:35=\frac{20}{35}=\frac{4}{7}$
 Ratio of number of girls to the total number of students is $=4:7$
(c) Ratio of number of boys to the total number of students
 $=15:35=\frac{15}{35}=\frac{3}{7}$
 Ratio of number of boys to the total number of students is $=3:7$