In this article we are deeply going to explore the concept of Ratio. Ratio is something that we all use in our day to day life but most of the times we are not aware of it. we put the concept of ratio into practice whenever we have to make a division of quantities and then compare the divided quantities to make a decision . this article will first strengthen your conceptual understanding about Ratio next will help you apply your knowledge through solved and unsolved examples.
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what is ratio
Ratio equals division Or Ratio is a comparison of two or more similar quantities .
below are given three examples related to the concept.Read them carefully
Example 1: 15 kg rice is to be distributed between aman and raman in 3:2 then what will the amount of rice aman and raman get ?
Aaman get 3 parts while raman get 2 parts of 15 kg.it means 3 part and 2 parts make 15 kg.
(3+2) part = 15 kg
⇒ 5 parts = 15 kg
⇒ 1 part = 3 kg
Amount of rice aman gets = 3 parts × 3 kg = 9 kg
Amount of rice raman gets = 2 parts × 3 kg = 6 kg
Therefore 15 kg is divided into 9 kg and 6 kg and the simplest ratio/division = 9 kg / 6 kg = 3/2
Example 2 : 5 pens is to be given to two children in 3:2 then first child gets 3 pens and second one gets 2 pens.
What if 12 pens is be given to 3 children in 1:2:3 then
1 part + 2 part + 3 part = 12 pens
6 part =12 pens
⇒1 part = 2 pens .
First child gets= 2 pens
Second child gets = 2 × 2 pens= 4 pens
Third child gets= 3× 2 pens = 6 pens
Example 3 : A 0.5 foot rope is cut into 4:2 then what will be the length(in inches ) of the longer part ?
0.5 feet = 0.5 × 6 = 12 inches
4 parts +2 parts = 6 parts
⇒ 6 parts = 12 inches
⇒ 1 part = 2 inches
length of the longer part = 4 part × 2 inches
= 8 inches
Conversion from Ratio to percentage
The following formula is used if the percentage of the first value to be found for a given Ratio.
Percentage of first value = \( \text{First value} \over \text{Sum of all values} \) ×100
Percentage of second value= \( \text{second value} \over \text{Sum of all values} \) ×100
In a bottle the Ratio of milk and water is 2:3 find the percentage of milk in the bottle
Total sum of quantities = 3+2 =5
Percentage of milk in the bottle =\( {2\over 5}×100 \)
=40%
Similarly If we are asked to find the percentage the of water in the bottle
Percentage of water = \( 3 \over 5 \) ×100
= 60%
Ratio questions with Illustration
Illustration 1 : What is the ratio of 8 to 4?
Illustration 2 : If a class has 10 boys and 15 girls, what is the ratio of boys to girls?
Illustration 3 : Simplify the ratio 12 : 18.
Illustration 4 : A bag has 5 red balls and 20 blue balls. What is the ratio of blue balls to red balls?
Illustration 5 : Write the ratio of 25 minutes to 1 hour.
What is proportion
when two ratios are equal they are said to in proportion. which means equivalency of two ratios is termed as proportion. let the ratio of a to b is - a : b and c to d is - c : d
If these two ratios are in proportion then we can write
\( {a\over b} = { c \over d} \) or \( a: b :: c : d \)
where \( ( ::) \) is used two show that two ratios are equal.
let's take a few examples to grasp it.
Example 1 : given 2 : 3 :: 4 : x then find the value of x .
2 : 3 \( \implies \) \( 2 \over 3 \)
4 : x \( \implies \) \( 4 \over x \)
since these two ratios are in proportion , we can equate them
\( { 2 \over 3 } = {4 \over x } \)
\( x = { 4 \times 3 \over 2} \)
\( \implies \) \( x = 6 \)
Example 2 : Charles had $20 and Wilson had 60$. They pooled their sum and purchased 160 kg sugar. How much sugar did Charles receive ?
The ratio of money invested by Charles and Wilson is :
\( {Charles \over Wilson } = { 20 \over 30 } \)
= \( {2 \over 3} \implies 2 : 3 \)
The ratio of money invested by Charles & Wilson is 2 : 3, hence the amount of sugar will also be distribued in 2 : 3 . Now divide 160 into 2 : 3
Total parts = 2 part + 3 part = 5 part
Charles' part = \( 2 \over 5 \)
Wilson's part = \( 3 \over 5 \)
The amount of Sugar Charles receives = \( {2 \over 5} \times \text{ Total Sugar} \)
= \( {2 \over 5} \times \text{160} = 64 \text{kg} \)
The amount of Sugar Wilson receives = \( {3 \over 5} \times \text{ Total Sugar} \)
= \( {3 \over 5} \times \text{160} = 96 \text{kg} \)
FAQs on Ratio & Proportion
If these two ratios are in proportion then we can write
\( {a\over b} = { c \over d} \) or \( a: b :: c : d \)
where \( ( ::) \) is used two show that two ratios are equal.
let's take a few examples to grasp it.
Example 1 : given 2 : 3 :: 4 : x then find the value of x .
2 : 3 \( \implies \) \( 2 \over 3 \)
4 : x \( \implies \) \( 4 \over x \)
since these two ratios are in proportion , we can equate them
\( { 2 \over 3 } = {4 \over x } \)
\( x = { 4 \times 3 \over 2} \)
\( \implies \) \( x = 6 \)
Example 2 : Charles had $20 and Wilson had 60$. They pooled their sum and purchased 160 kg sugar. How much sugar did Charles receive ?
The ratio of money invested by Charles and Wilson is :
\( {Charles \over Wilson } = { 20 \over 30 } \)
= \( {2 \over 3} \implies 2 : 3 \)
The ratio of money invested by Charles & Wilson is 2 : 3, hence the amount of sugar will also be distribued in 2 : 3 . Now divide 160 into 2 : 3
Total parts = 2 part + 3 part = 5 part
Charles' part = \( 2 \over 5 \)
Wilson's part = \( 3 \over 5 \)
The amount of Sugar Charles receives = \( {2 \over 5} \times \text{ Total Sugar} \)
= \( {2 \over 5} \times \text{160} = 64 \text{kg} \)
= \( {3 \over 5} \times \text{160} = 96 \text{kg} \)
FAQs on Ratio & Proportion
Q1: What is the unit of Ratio?
Ans : Since Ratio is a fraction, hence there is no unit of it.
Q 2 : Are Ratio and Proportion the same?
Ans : No Both the terms refers to different things. Ratio compares two quantities whereas proportion compares two ratios.
Q3 : Can Ratio be Positive or Negative?
Ans : Yes ratio can be either positive or negative. But mostly in maths it is found postive.
Q 4 : How to convert a fraction to Percentage?
Ans : To convert the given fraction into percentage multiply it with 100.