Class 8 Maths Chapter 8 Notes - Comparing Quantities

What is Ratio

When we compare two quantities having the same unit, the comparison is referred as ratio. This relation gives us the number of times one quantity is equal to the other. In simple words, it is a representation that expresses two quantities as a fraction.

The comparison of any two numbers/quantities using ratio is only possible when they have the same unit. The sign used to denote a ratio is ‘:’.
A ratio can be written as a fraction, say 3:4 can be written as 3/4.

The first term of a ratio is called the antecedent and the second term is called the consequent.

What is Percentage

The part 'cent' of the word 'percent' means '100'; therefore, the term 'percent' means 'out of hundred'.

A percentage is a part of a whole quantity. It is a number without any unit or dimension. In fractional form, if the denominator is 100, then the numerator is the percentage and is represented by the symbol ‘%', and we read it as ‘percent'.

A percentage can be written as a fraction, say 30% can be written as 30/100, which can be further simplified as 3/10.

To calculate the increase or decrease of a quantity in terms of percentage, we use the following formulae-

Increase in percent =
Decrease in percent =

Discount, Profit, & Loss

Discount

Discount is the reduction in the price of goods or services offered by sellers at the marked price.

• Discount = Marked price – Selling price
• Discount% = Discount / Marked price × 100
Discount percentage is always calculated on the 'Marked price'.

Profit & Loss

When the selling price is greater than the cost price, we earn a profit. However, when the cost price is greater than the selling price, we incur a loss.

NCERT Solutions for Class 8 Maths Chapter 8
NCERT Solutions Class 8 Maths Chapter 8
NCERT Solutions Class 8 Maths Exercise 8.1
NCERT Solutions Class 8 Maths Exercise 8.2
NCERT Solutions Class 8 Maths Exercise 8.3

Formulae:

• Profit = Selling price – Cost price
• Profit % = Profit / Cost price × 100
• Loss = Cost price – Selling price
• Loss % = Loss / Cost price × 100
• Selling Price = 100 + profit % / 100 × Cost price
• Selling Price = 100 – Loss % / 100 × Cost price
• Cost Price = 100 / 100 + Profit % × Selling price
• Cost Price = 100 / 100 – Loss % × Selling price

Let us see an example to understand, profit, loss, and discount.

A shopkeeper allows his customers 10% off on the marked price of goods and still gets a profit of 20%. What is the actual cost to him of an article marked ₹500?

MP of the article = ₹500
Discount = 10%
Discount = 10% of ₹500
= 10/100 × ₹500
= ₹50
SP = MP – Discount
= ₹500 − ₹50
= ₹450
Profit% = 20%

Thus, the CP of the article is ₹375.

Tax

Tax is the money that people have to pay to the government. Sales tax is paid by the customer on the total amount of the product.
VAT - Value added tax. It is the tax that is already included in the price of any item. From 1 July 2017, the Government of India introduced a new tax, GST (Goods and services tax), which is levied on the supply of goods or services, or both.

Let’s work on this example to understand it.

Suppose, Anuj purchased a shirt which costs ₹4800 including a tax of 20%. What is the original cost of the shirt before VAT was added?

If we let the original price be ₹100, then price after tax included will be ₹120 as 20% tax is applicable on ₹100.

It means if the price inclusive of tax is ₹120 then the original price is ₹100.

Similarly, if the price inclusive of tax is ₹4800 then the original price will be

100 / 120 × 4800
= 4000

Therefore, the original price of the shirt is ₹4000.

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Compound Interest

The interest calculated on both the principal amount and the interest earned is called compound interest. The amount of the principal increases with time, as the interest payable, is added to it.

The formula for calculating compound interest is-

Amount(A) =

✍ Also learn: How to Calculate Compound Interest

Compound Interest = A – P
Where, P = Principal; r = Rate of interest; n = Number of years
If the rate of interest is negative, that is, if the amount is decreasing over time, then the formula for calculating compound interest will be-

Amount(A) =
Compound Interest = A – P
If the rate of interest is not constant, that is, the amount increases to r1 during the first year, again it increases to r2 during the second year, but decreases during the third year to r3, then, in this case, the formula for calculating compound interest will be-

Amount(A) =
Compound Interest = A – P
Many times, it happens that the interest is compounded half-yearly or quarterly.
In case of interest compounded half-yearly, the time will become double and the rate of interest will get half.

Amount(A) =
Compound Interest = A – P
Where, P = Principal, r = Rate of interest compounded half-yearly; n = number of years
In the case of interest compounded quarterly, the time becomes four times and the rate of interest gets divided by four.

Amount(A) =
Compound Interest = A – P
Let us solve a real-life application problem.
A city had 22,000 birds in 2012. Its population declined at a rate of 8% per annum. What was the total population of birds at the end of the year 2016?
Population in 2012, P = 22,000; Time, n = 4 years; Rate of decline, r = 8%
Therefore, population at the end of the year 2016
=
∴ The population of birds at the end of the year 2016 was 15761.

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