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 ratio of red candies to green candies, we can write:

Red candies : Green candies = 10 : 5

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 = 105 = 2

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

Instructions

Since Basket contains only apples and oranges,

So, percentage of apples + percentage of oranges =

(or) percentage of apples + 20 = 100

(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:

1. The ratio of the number of girls to the number of boys in the class?

2. The cost per head if two teachers are also going with the class?

3. 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.

So, the number of boys = – = .

Hence, ratio of the number of girls to the number of boys is 18 : 12 or 1812 =

32 is written as 3 : 2 and read as 3 is to 2.

2. To find the cost per person.

Transportation charge = Distance both ways × Rate

= ₹ 55×2×12

₹ 110 × 12 = ₹

Total expenses= Refreshment charge + Transportation charge

= ₹ 4280 + ₹ 1320

= ₹

Total number of persons = 18 girls + 12 boys + 2 teachers

= 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 = ₹ 560032 = ₹ .

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

To find the percentage of distance:

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

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 12 hour to 1 12 hours. The distribution of parents according to the time for which, they said they helped is given in the adjoining figure:

20% helped for more than 1 1/2 hours per day

30% helped for 1/2 hour to 1 1/2 hours

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 1/2 hours?

Let the total number of parents surveyed be N.

(i) We know that 30% of the total number of parents surveyed helped for 12 hour to 1 12 hours. Thus:

30% of N = 90 ⇒ × N = ⇒ N = 0.390 =

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 = × 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 12 hours. Thus:

20% of 300 = × 300 =

So, the number of parents who said that they helped for more than 1 1/2 hours is 60.