# Introduction

## Recalling Ratios and Percentages

Imagine you have a bag of colorful candies, and you find that you have 10 red candies and 5 green candies. **A ratio is a way of comparing two quantities**, in this case, the number of red candies to the number of green candies.

To express the

**Red candies** : **Green candies** = :

This means that **for every 10 red candies, there are 5 green candies**. You can also think of it as saying that there are 2 red candies for every green candy.

**Using Fractions to Represent Ratios**

We can also use fractions to represent ratios. For example, the ratio of red candies to green candies can be written as:

**Red candies** : **Green candies** = =

This means that **there are 2 red candies for every 1 green candy**.

**the number of apples is** times the number of oranges. This comparison can also be done using percentages.

There are 5 oranges out of 25 fruits. So, percentage of oranges is:

[**Denominator made 100**]

**By unitary method:** Out of 25 fruits, number of oranges are 5.

So out of 100 fruits, number of oranges:

Since Basket contains only apples and oranges,

So, percentage of apples + percentage of oranges =

(or) **percentage of apples** +

(or) **percentage of apples** = 100 – 20 =

**Thus, the basket has % oranges and % apples.**

**Example 1: A picnic is being planned in a school for Class VII. Girls are 60% of the total number of students and are 18 in number.**

The picnic site is 55 km from the school and the transport company is charging at the rate of ₹ 12 per km. The total cost of refreshments will be ₹ 4280.

**Can you tell:**

**The ratio of the number of girls to the number of boys in the class?****The cost per head if two teachers are also going with the class?****If their first stop is at a place 22 km from the school, what per cent of the total distance of 55 km is this? What per cent of the distance is left to be covered?**

**Solution:**

**1. To find the ratio of girls to boys**

Ashima and John came up with the following answers.

They needed to know the number of boys and also the total number of students.

**Ashima did this**

Let the total number of students

be x. 60% of x is girls.

Therefore, 60% of x =

(or)

**Thus, number of students = 30.**

**John used the unitary method**

There are 60 girls out of 100 students.

There is one girl out of

**So, 18 girls are out of how many students ?**

Number of students =

So, the number of boys =

**Hence, ratio of the number of girls to the number of boys is : or **

**2. To find the cost per person.**

Transportation charge = Distance both ways × Rate

= ₹

₹ 110 × 12 = ₹

**Total expenses = Refreshment charge + Transportation charge**

= ₹

= ₹

Total number of persons =

=

Ashima and John then used unitary method to find the cost per head. For 32 persons, amount spent would be 5600. The amount spent for 1 person = ₹

**3. The distance of the place where first stop was made = 22 km**

To find the percentage of distance:

**Ashima used this method:**

**She is multiplying the ratio by 100100 = 1 and converting to percentage**.

**John used the unitary method:**

Out of 55 km, 22 km are travelled.

Out of 1 km,

Out of 100 km,

**That is 40% of the total distance is travelled**.

Both came out with the same answer that the distance from their school of the place where they stopped at was 40% of the total distance they had to travel.

**Therefore, the percent distance left to be travelled = % – % = %.**

### Try These

### Q1

**In a primary school, the parents were asked about the number of hours they spend per day in helping their children to do homework. There were 90 parents who helped for **

**20% helped for more than 1 **

**30% helped for **

**50% did not help at all**

**Using this, answer the following:**

**(i) How many parents were surveyed?**

**(ii) How many said that they did not help?**

**(iii) How many said that they helped for more than 1 **

### Sol

Let the total number of parents surveyed be N.

(i) We know that 30% of the total number of parents surveyed helped for

30% of N = 90 ⇒

**So, the total number of parents surveyed is 300.**

(ii) We know that 50% of parents did not help at all. Thus:

50% of 300 =

**So, the number of parents who said that they did not help is 150.**

(iii) We know that 20% of parents helped for more than 1

20% of 300 =

**So, the number of parents who said that they helped for more than 1 **