Free Ratio and Proportion 03 Practice Test - 6th grade 

The unitary method is a method in which we find the value of one unit (by division) and calculate the value of multiple units using the single unit (by multiplication). 

The ratio is a method in which we compare the two similar quantities by dividing them and check how much one value contains or is contained within the other.

The ratio of their ages is 12 : 15 or 4 : 5.
So, the money has to be divided in the ratio 4 : 5.

Let the shares be $4x$ and $5x$ respectively.
Now, $4x+5x=9x$
Thus, $9x=1800⟹x=200$

Hence, the share for the 12 year old son is
$4x$ = $4\times 200$  = ₹ 800

The share for the 15 year old son is
$5x$ = $5\times 200$  = ₹ 1000

Grandfather's present age is 72 years.
Grandson's present age is 12 years.

After 8 years,
grandfather's age would be 72 + 8 = 80 years
and grandson's age would be 12 + 8 = 20 years.

So, after 8 years, the ratio of grandfather's age to grandson's age  would be $\frac{80}{20}=\frac{4}{1}=4:1$.

The ratio of areas of a circular and rectangular field is 1:2, which implies that the area of the rectangular field is twice the area of the circular field.
Given, area of circular field is $50m^2$.
$⟹$Area of the rectangular field
        $=2\times 50=100m^2$

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.

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 

$\frac{500}{70}\times 7=50km$

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 
$\frac{714}{7}\times 21=₹2142$