comparing quantities class 8 Example 1

Class VII Picnic Math Challenge

The Problem

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?

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

Step 1: Find the total number of students.

We know that 60% of the total students are girls, and this number is 18.

`60% of Total Students = 18`

( 60100 ) * Total = 18

Total = 18 * ( 10060 )

Total = 18 * ( 106 )

Total = 3 * 10 = 30

There are 30 total students.

Step 2: Find the number of boys.

`Boys = Total Students - Girls`

`Boys = 30 - 18 = 12`

There are 12 boys.

Step 3: Find the ratio of girls to boys.

`Ratio = Girls : Boys`

`Ratio = 18 : 12`

To simplify, divide both numbers by their greatest common divisor (which is 6):

`18 ÷ 6 = 3`

`12 ÷ 6 = 2`

The ratio of girls to boys is 3 : 2.

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

Step 1: Find the total number of people.

`Total People = Total Students + Teachers`

`Total People = 30 + 2 = 32`

There are 32 people going on the picnic.

Step 2: Find the total transport cost.

The distance is 55 km *from* the school. The bus must travel there AND back.

`Total Distance = 55 km (to) + 55 km (back) = 110 km`

`Transport Cost = 110 km * ₹12/km`

Transport Cost = ₹1320

Step 3: Find the total cost of the picnic.

`Total Cost = Transport Cost + Refreshment Cost`

`Total Cost = ₹1320 + ₹4280`

Total Cost = ₹5600

Step 4: Find the cost per head.

Cost per Head = ( ₹560032 )

The cost per head is ₹175.

3. What per cent of the total distance is 22 km? What per cent is left?

Part 1: Per cent of distance covered.

The formula is `(Part / Whole) * 100`.

( 2255 ) * 100

First, simplify the fraction `22/55` by dividing both sides by 11:

22 ÷ 1155 ÷ 11 = 25

Now, calculate the percentage:

( 25 ) * 100 = 0.4 * 100 = 40%

The first stop is 40% of the total distance.

Part 2: Per cent of distance left.

You can solve this in two ways:

Method A (Simple): Subtract the covered percentage from 100%.

`100% - 40% = 60%`

Method B (Verification): Calculate the remaining distance first.

`Distance Left = 55 km - 22 km = 33 km`

Now, find what percentage 33 km is of 55 km:

( 3355 ) * 100

Simplify the fraction (divide by 11): 35

( 35 ) * 100 = 0.6 * 100 = 60%

There is 60% of the distance left to be covered.