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Chapter 11: Ratio and Proportion

    Introduction

    Comparing quantities with different units

    Ratio

    Same ratio in different situations

    Division of a given quantity in a given ratio

    Proportion

    Unitary Method

    Exercise 11.1

    Exercise 11.2

    Exercise 11.3

    Exercise 11.4

    What Have We Discussed

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Chapter 11: Ratio and Proportion > Same ratio in different situations

Same ratio in different situations

Length of a room is 30 m and its breadth is 20 m. So, the ratio of length of the room to the breadth of the room = = =

There are 24 girls and 16 boys going for a picnic. Ratio of the number of girls to the number of boys = 2416= 32 =

The ratio in both the examples is 3:2.

Note: The ratios 30 : 20 and 24 : 16 in lowest form are same as 3 : 2. These are "equivalent ratios".

Another Example: Ravi and Rani started a business and invested money in the ratio 2 : 3. After one year the total profit was Rs 4,00,000.

Ravi said “we would divide it equally”, Rani said “I should get more as I have invested more”.It was then decided that profit will be divided in the ratio of their investment.

Here, the two terms of the ratio 2 : 3 are and .

Sum of these terms = 2 + 3 =

What does this mean?

This means if the profit is 5 rupees then Ravi should get 2 rupees and Rani should get 3 rupees. Or, we can say that Ravi gets 2 parts and Rani gets 3 parts out of the 5 parts.

i.e., Ravi should get 25 of the total profit and Rani should get 35 of the total profit.

If the total profit were 500 rupees,

Ravi would get 25× 500 = rupees

and Rani would get 35× 500 = rupees.

Now, if the profit were 4,00,000 rupees could you find the share of each?

Ravi’s share = 25× 4,00,000 = rupees

and Rani’s share = 35× 4,00,000 = rupees.

Let us look at the kind of problems we have solved so far.

1. Find the ratio of number if there are 10 notebooks and 4 books in the bag.

Solution :

We have notebooks and books in the bag.

Ratio = Number of notebooksNumber of books = 104 =

2. Find the ratio of number if there are 16 desk and 40 chairs.

Solution :

We have: desks and chairs

Ratio = Number of desksNumber of chairs = 1640 =

3. Find the number of students above twelve years of age in your class. Then, find the ratio of number of students if there are 20 students in the class and 4 students.

Solution :

We have: Number of students above twelvw years of age =

And total number of students =

Ratio = Number of students above 12Total number of students = 420 =

4. If there are 6 windows and 3 door then the ratio of the number of doors and the number of windows.

Solution :

We have: doors and windows

Ratio = Number of doorsNumber of windows = 36 =

5. A rectangle has length 7 cm and breadth of 2 cm then ratio of its length to its breadth.

Solution :

We have: Length = cm and Breadth = cm

Ratio = LengthBreadth =

Length and breadth of a rectangular field are 50 m and 15 m respectively. Find the ratio of the length to the breadth of the field.

Solution :

Length of the rectangular field = m

Breadth of the rectangular field = m

The ratio of the length to the breadth is

We simplify this ratio by dividing the numerator and denominator by the greatest common factor for the numbers 15 and 50 i.e. .

Thus, the ratio can be written as = 5015 = 50/515/5 = =

Thus, the required ratio is 10:3.

Find the ratio of 90 cm to 1.5 m.

Solution :

The two quantities are not in the same units. Therefore, we have to convert them into same units.

1.5 m = 1.5 × cm = cm.

Therefore, the required ratio is .

Similar to the previous example, we can further simplify this ratio by dividing the numerator and denominator by the greatest common factor (for 90 and 150) which will be .

Thus, 90150 =

Required ratio is 3:5.

There are 45 persons working in an office. If the number of females is 25 and the remaining are males, find the ratio of:

(a) The number of females to number of males.

(b) The number of males to number of females.

Solution :

Number of females =

Total number of workers =

Number of males = – =

Therefore, the ratio of number of females to the number of males = = (Simplify with the help of greatest common factor)

And the ratio of number of males to the number of females = =

Give two equivalent ratios of 6 : 4.

Solution :

Ratio 6 : 4 = 64 = 6 × 24 × 2 = =

Therefore, 12:8 is an equivalent ratio of 6:4

Similarly, the ratio 6 : 4 = 6 / 24 / 2 =

So, 3:2 is another equivalent ratio of 6 : 4.

Therefore, we can get equivalent ratios by multiplying or dividing the numerator and denominator by the same number.

Fill in the missing numbers : 1421 = (_ / 3) = (6 / _ )

Solution :

In order to get the first missing number, we consider the fact that 21 = 3 ×

.i.e. when we divide 21 by 7 we get 3. This indicates that to get the missing number of second ratio, 14 must also be by 7.

When we divide, we have, 14÷7 =

Hence, the second ratio is 23.

Similarly, to get third ratio we multiply both numerator and denominator of second ratio by .

As 2 × 3 will give us the desired given numerator in the third ratio i.e. 6, we can deduce that: the third ratio is .

Therefore, 1421 = 23 = 69 (These are all equivalent ratios)

Ratio of distance of the school from Mary’s home to the distance of the school from John’s home is 2 : 1.

(a) Who lives nearer to the school?

(b) Complete the following table which shows some possible distances that Mary and John could live from the school.

Distance from Mary’s home to school(in km.)Distance from John’s home to school(in km.)
105
4
4
3
1

Divide Rs 60 in the ratio 1:2 between Kriti and Kiran.

Solution :

The two parts are 1 and 2.

Therefore, sum of the parts = 1 + 2 = .

This means if there are Rs 3 , Kriti will get Rs 1 and Kiran will get Rs 2. Or, we can say that Kriti gets part and Kiran gets parts out of every 3 parts.

Therefore, Kriti’s share = × 60 =

And Kiran’s share = × 60 =