Comparing Quantities: Explanation, Formula

In a supermarket we compare the buying goods, in the class, our marks are compared, etc. There are various other quantities that are measured like weight, heights, speed, distance, quantity, etc. To make a comparison, we require quantities of the same unit. We can’t compare a person’s height with a person’s weight. There should always be a common reference point for comparison. Similarly, there are standard ways of comparing the quantities that we’ll be discussing in this article below.

Key Terms: Ratio, Percentage, Profit & Loss, Discount, Sales Tax, Value Added Tax, Simple Interest, Compound Interest

Also read: Isosceles Triangle Theorems

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Ratio 

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The ratio is referred to as comparing two quantities using fractions. If two fractions are equal then the given ratios are considered to be equivalent.

Examples of Ratio

Let’s consider a basket full of 2 fruits i.e, 20 apples and 5 oranges. 

• The ratio of the number of oranges to the number of apples will be written as 5:20. 
• Since the ratio should always be in the simplest form, so we can compare it using fraction, then it will be written as 5/20 = 1/4. The number of oranges is 1/4th the number of apples. In terms of ratio, it will be written as 1:4, which is read as 1 is to 4.

• Similarly, the number of apples to the number of oranges will be 20/5 = 4/1. This means the number of apples is 4 times the number of oranges. It will be written as 4:1 in the form of a ratio.

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Percentage 

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It is a fraction with its denominator as 100. Percentage means per 100 and is denoted by %.

Example for Percentage

There are 25 fruits in a basket, out of which 5 are oranges.

• So to find the percentage of oranges, the denominator should be 100. So, 52544 = 20100 = 20%
• If we use the unitary method then, out of 25 fruits there are 5 oranges and out of 100 fruits, there will be 525100=20 oranges.

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Profit & Loss

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To compare quantities through profit and loss, one should understand the following terms:

1. Cost Price (CP) - The amount at which an article has been purchased is called cost price. It could be the price at which a shopkeeper buys products from a wholesaler or a distributor. It also includes overhead charges like the transportation cost, expenditure on repair, etc.
2. Selling Price (SP) - The amount at which an article is sold is known as the selling price. This could be the price at which a shopkeeper sells the product to the customer.
3. Profit - When the selling price of the product is more than the cost price, then there is a profit. It could be equal to the difference between the selling price and cost price. 

Profit = SP-CP

4. Loss - When the cost price of the product is more than the selling price, then there is loss. It is equal to the difference between the cost price and the selling price. 

Loss=CP-SP

Important Formulas

In case of profit:

In case of loss:

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Discount

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• When there is a reduction in the marked price (MP) of an article, then this reduced amount is called a discount. It is usually given to attract customers to buy the product or to promote sales of the goods.
• Marked Price (MP) is also known as the printed price or tagged price of the article.
• Discounts can be calculated by subtracting the sale price from the marked price.

Discount =Marked Price (MP)-Sale Price

Important Formulas

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Sales TAX, Value Added Tax and GST

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There are 3 types of taxes that are always implemented in the form of percentages and will apply to the sales of goods and services.

• Sales Tax (ST) - The tax charged by the government on the sale of an item is the sales tax. It is added to the value of the bill and is collected by the shopkeeper from the customers and then given to the government.

• Value Added Tax (VAT) - This is a tax implemented by the government on various products. Different items carry different VAT and are included in the selling price of the article.

• Goods and Service Tax (GST) - It is a tax that is levied on the supply of goods or services or both. This tax was implemented by the Government of India on July 1, 2017.

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Interest

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• Whenever we deposit money in the bank or post office for a certain period of time, then the bank or the post office pays some extra money, which is known as interest.
• Interest is also paid by people when they borrow money from someone and pay extra money for using the borrowed money.

Simple Interest

For calculating simple interest we need to understand the following terms.

• Principal (P) - It is the amount that a person deposits in the bank or lends someone.

• Time (T) - It is the time duration for which the money has been deposited.

• Rate of Interest (R%) - It is the percentage at which the interest is being offered. It is generally given in percent per year.

• Amount (A) - It is the sum of principal and interest.

Important Formulas

Compound Interest

Compound interest is different from simple interest. 

• The borrower and lender fix the amount for a certain period of time. This fixed time is called the conversion period.
• The principal changes after each fixed unit of time because the interest accrued during the fixed unit of time is added to the principle and the amount obtained is considered as the principal for the next unit of time.
• The difference between the amount and the money borrowed is calculated as compound interest.

Important Formulas

Here, Principal = P, Rate = R%, Time = n years, Amount = A

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Things to Remember

• The two quantities that are being compared should have the same unit.
• To compare two ratios, it
• Two ratios can be compared by transforming them into a fraction.
• Quantities can also be compared by percentage, which means the denominator is 100.
• The buying price of the product is called cost price (CP).
• The selling price of the product is called selling price (SP).
• When the selling price is more than the cost price, then it is profit.
• When the cost price is higher than the selling price, then it is a loss.
• When there is a reduction in the marked price, then the product is at a discount.
• The borrowed money is referred to as principal (P).
• The extra money paid for using the borrowed money is called Interest (I).
• The period for which the money is borrowed is called the Time Period (T).
• The percentage of interest paid on the borrowed money is called the Rate of Interest (R).
• The total sum of principal and interest is called Amount (A).

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