Free Ratio and Proportion 02 Practice Test - 6th grade 

If two ratios are equal or equivalent then we say that they are in proportion.

If two quantities have different units then we cannot compare them by the method of ratio. A ratio is a method of comparison of two similar quantities by using the method of division.

Number of pink balls = 2 
Total number of balls = 2 + 3 + 5 = 10
$\therefore$ Ratio of pink balls to the total number of balls 
$=2:10=\frac{2}{10}=\frac{1}{5}=1:5$

We know, to compare two quantities, the units must be the same.
So, here we either convert meter to a centimeter or vice-versa.
Given,
Length of the table = 2 m = 200 cm
Breadth = 50 cm
Hence, the required ratio
$=200:50=\frac{200}{50}=\frac{4}{1}=4:1$

The ratio is the method of comparison between two similar quantities having the same unit.

Length = 2 m = 2000 mm and diameter = 1 mm 

Hence ratio of the length of rope to its diameter is

$\frac{2000}{1}=2000:1$

Two ratios are said to be in proportion if they are equivalent or equal.
Here,
$\frac{4}{5}=\frac{4\times 3}{5\times 3}=\frac{12}{15}$

Hence, 4 : 5 :: 12 : 15, are in proportion.

Also product of 1st and 4th term should be equal to product of 2nd and 3rd term, which is only satisfied by 4 : 5 :: 12 : 15, i.e.,
$4\times 15=5\times 12=60$.

For rest of them the product of 1st and 4th term is not equal to the product of 2nd and 3rd term.
 

The cost of 12 bananas = ₹ 24,
So, the cost of one banana =
$\frac{₹24}{12}=₹2$

The cost of 10 apples = ₹ 100,
So, the cost of one apple =
$\frac{₹100}{10}=₹10$

Therefore, the ratio of the cost of an apple to that of a banana = ₹ 10 : ₹ 2 = 5 : 1.

So, an apple is five times costlier than a banana.

$\text{Shekhar's run rate =}\frac{96}{6}=16\text{runs per over .}$

$\text{Nitish's run rate =}\frac{102}{6}=17\text{runs per over .}$​​​​​
​​​​​​​
Hence Nitish's run rate is greater than that of Shekhar.

The cost of 20 envelopes = ₹50.
$\therefore$ The cost of one envelope
 $=\frac{50}{20}$
= ₹ 2.5

One envelope costs ₹2.5.
So, for ₹10,  the number of  envelopes that can be purchased is equal to $\frac{10}{2.5}=4$

Let the fourth proportion be $x$.
Then, 1.2, 1.6, 7.2, $x$ are in proportion.

Product of means = Product of extremes
$\Rightarrow 1.6\times 7.2=x\times 1.2$
$\Rightarrow 1.2x=1.6\times 7.2$
$\Rightarrow x=\frac{1.6\times 7.2}{1.2}$
$\Rightarrow x=9.6$