# NCERT Solutions for Class 8 Maths Chapter 8 : Comparing Quantities

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## Chapter 8 : Comparing Quantities

### 8.1 Recalling Ratios And Percentages

We know, ratio means comparing two quantities. A basket has two types of fruits, say, 20 apples and 5 oranges. Then, the ratio of the number of oranges to the number of apples = 5 : 20.
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 Rs 12 per km. The total cost of refreshments will be Rs 4280.
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?

### 8.2 Finding The Increase Or Decrease Per Cent

We often come across such information in our daily life as. (i) 25% off on marked prices (ii) 10% hike in the price of petrol Let us consider a few such examples. Example 2: The price of a scooter was Rs 34,000 last year. It has increased by 20% this year. What is the price now?

### 8.3 Finding Discounts

Discount is a reduction given on the Marked Price (MP) of the article. This is generally given to attract customers to buy goods or to promote sales of the goods. You can find the discount by subtracting its sale price from its marked price. So, Discount = Marked price – Sale price

### 8.4 Prices Related To Buying And Selling (profit And Loss)

For the school fair (mela) I am going to put a stall of lucky dips. I will charge Rs 10 for one lucky dip but I will buy items which are worth Rs 5.
So you are making a profit of 100%.
No, I will spend Rs 3 on paper to wrap the gift and tape. So my expenditure is Rs 8. This gives me a profit of Rs 2,
Sometimes when an article is bought, some additional expenses are made while buying or before selling it. These expenses have to be included in the cost price. These expenses are sometimes referred to as overhead charges. These may include expenses like amount spent on repairs, labour charges, transportation etc.

### 8.5 Sales Tax/Value Added Tax

The teacher showed the class a bill in which the following heads were written.
1.ST means Sales Tax, which we pay when we buy items.
2.This sales tax is charged by the government on the sale of an item. It is collected by the shopkeeper from the customer and given to the government. This is, therefore, always on the selling price of an item and is added to the value of the bill. These days however, the prices include the tax known as Value Added Tax (VAT).

### 8.6 Compound Interest

You might have come across statements like “one year interest for FD (fixed deposit) in the bank @ 9% per annum” or ‘Savings account with interest @ 5% per annum’. Interest is the extra money paid by institutions like banks or post offices on money deposited (kept) with them. Interest is also paid by people when they borrow money. We already know how to calculate Simple Interest.

### 8.7 Deducing A Formula For Compound Interest

Zubeda asked her teacher, ‘Is there an easier way to find compound interest?’ The teacher said ‘There is a shorter way of finding compound interest. Let us try to find it.’ Suppose P1 is the sum on which interest is compounded annually at a rate of R% per annum. So, Zubeda said, but using this we get only the formula for the amount to be paid at the end of n years, and not the formula for compound interest. Aruna at once said that we know CI = A – P, so we can easily find the compound interest too.

### 8.8 Rate Compounded Annually Or Half Yearly (semi Annually)

You may want to know why ‘compounded annually’ was mentioned after ‘rate’. Does it mean anything? It does, because we can also have interest rates compounded half yearly or quarterly. Let us see what happens to Rs 100 over a period of one year if an interest is compounded annually or half yearly.
Time period and rate when interest not compounded annually The time period after which the interest is added each time to form a new principal is called the conversion period. When the interest is compounded half yearly, there are two conversion periods in a year each after 6 months. In such situations, the half yearly rate will be half of the annual rate. What will happen if interest is compounded quarterly? In this case, there are 4 conversion periods in a year and the quarterly rate will be one-fourth of the annual rate.

### 8.9 Applications Of Compound Interest Formula

There are some situations where we could use the formula for calculation of amount in CI. Here are a few.
(1) Increase (or decrease) in population.
(2) The growth of a bacteria if the rate of growth is known.
(3) The value of an item, if its price increases or decreases in the intermediate years.

### Smartur

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