The bus travels 500 km with 70 litres of petrol.
Hence, with one litre it can travel
$\frac{500}{70}km.$
$\therefore$ with 7 litres, the bus will cover a distance of 
$\frac{500}{70}\times 7=50km$

The number of boys in the class is 30 and number of girls in the class is 60.
$\therefore$ Total number of students is equal to 30 + 60 = 90.
Ratio of number of boys to the total number of students is equal to $\frac{30}{90}=\frac{30÷30}{90÷30}=\frac{1}{3}=1:3$

Equivalent or equal ratios form a proportion. So, the first two given options are equivalent as they are equal in their simplest forms.
Alternatively, if the numbers are in proportion, then the product of 1st and 4th term is equal to product of 2nd and 3rd term.
Here, in first option this is satisfied as $13\times 42=14\times 39=546$
Also in second option $11\times 3=1\times 33=33$
In third and fourth option the given condition is not satisfied.

As Utkarsh pays ₹ 7500 for three months.
His monthly rent is
$\frac{7500}{3}=₹2500$
Hence annually, he has to pay
$2500\times 12$
= ₹ 30,000

The cost of one metre of cloth would be
$₹\frac{714}{7}$.
Hence 21 m of cloth would cost 
$\frac{714}{7}\times 21=₹2142$

A ratio is a method by which two similar quantities are compared by using division.

Two or more quantities can be compared only when they have same unit. If they are not, they must be converted into the same units.
Example: Weight in gram cannot be compared to length in metre and weight in grams and kilograms can be compared only when kilograms is converted into grams or grams into kilograms so that both will be in same unit.

Ratio is a method of comparing two quantities having the same unit,
2 m = 200 cm
Hence, the ratio of the length of the snake to crocodile would be
$\frac{10}{200}=\frac{1}{20}=1:20$

Partnership is directly proportional to the amount invested. As amount invested increases patnership(profit) increases. Hence they are directly proportional.

There are 30 days in the month of April. So, the ratio of holidays to the number of days in April would be
$\frac{6}{30}=\frac{1}{5}=1:5$