2. Ratio
Introduction :
We use ratio for to do comparison between two quantities.
e.g. Time to reach to the destination, age of family members, score in
cricket match, marks in the examination, income of persons, sales of
different goods etc.
Even whenever we invest money into the bank we think of the interest
rates per annum. Suppose in a family out of two children namely Ajay
and Rakesh , Ajay got 60 marks out of 80 and Rakesh got 30 marks out
of 50.Then how do we decide whose performance is better? Then by
taking the quotient scored marks /total marks we can easily compare
their performance .Here we are using ratio to do the comparison of
performance of Ajay and Rakesh.
Note:
Ratio is used only when the unit of measurement of two quantities is
same.
3. Ratio
Definition:
If x and y are magnitudes of similar type and with
same units then the quotient is called the ratio of x
to y .
Notation: The ratio of x to y is denoted by x:y.
Note:
1)Ratio has no any unit.
2)In the ration x:y, x is called antecedent and y is
called consequent.
3)Ratio remains unchanged if we multiply/divide ratio
by same number.
y
x
4. Continued Ratio
Continued Ratio:
The ratio between the quantities of three or more
quantities of similar type is called continued ratio.
Notation:
The continued ratio of three similar type of quantities
x,y,z is denoted by x:y:z.
5. Ratio:Examples
Example :
Ratio of two numbers is 3:5 and their sum is 232.Find
the numbers.
Solution:
Let the common ratio be x ,so the given numbers are
3x and 5x.
Therefore we get 3x+5x =232
⇒ 8x = 232
⇒ x=29
∴ we get 3x = 3⨯29 = 87 and 5x = 5⨯29=145 .
∴The required numbers are 87 & 145.
6. Ratio:Examples
Example :
Ratio of two numbers is 4:7 and the bigger
number is 147.Find the smaller number.
Solution:
Let the common ratio be x ,so the given
numbers are 4x and 7x.
The bigger number is 147 i.e. 7x=147
⇒x = 21
∴ We get the smaller number as 4x = 4⨯21=84 .
