Chapter 8: Comparing Quantities

Chapter 8: Comparing Quantities

By Ananya Goyal

Recalling 3 quantities

Subject | Maths

Ananya Goyal

Fraction to Percentage

Subject | Maths

Ananya Goyal

Ratio to Percentage

Subject | Maths

Ananya Goyal

Decimal to Percentage

Subject | Maths

Ananya Goyal

Finding Percentage of Number

Subject | Maths

Ananya Goyal

Percentage Change

Subject | Maths

Ananya Goyal

​Percentage change can be positive or negative. If the new value is less than original value, then the difference on subtracting the old value from the new ​value will be negative.

Profit percentage

Subject | Maths

Ananya Goyal

​Profit percent is ALWAYS calculated on C.P. not on S.P or M.P.​

Loss Percentage

Subject | Maths

Ananya Goyal

​Loss percent is ALWAYS calculated on C.P. not on S.P.​ or M.P.

QUESTIONS

Factorisation

Multiple Choice

Convert 13 : 75 to percent

• 17.33 %

• 17 %

• 18.33 %

• 16.36 %

Multiple Choice

Convert $$\frac{7}{25}$$  to percent

• 35 %

• 21 %

• 28 %

• 28.33 %

Multiple Choice

Express 32% as decimal

• 3.2

• 0.32

• 32

• $$\frac{32}{10}$$  

Multiple Choice

Find the number a, if 8.4% of a is 42.

• 50

• 500

• 5

• 100

Multiple Choice

The price of a motorcycle was Rs. 34,000 last year. It has increased by 20% this year. The price of motorcycle now is:

• Rs. 36,000

• Rs. 38,800

• Rs. 40,800

• Rs. 32,000

Multiple Choice

 If an article is sold for Rs. 100, then there is a gain of Rs. 20, which of the following is the gain percent?

• 25%

• 22%

• 20%

• 16%

Multiple Choice

On which of the following profit percent or loss percent is calculated?

• S.P.

• C.P.

• M.P.

• None of these

Discount

1) Marked price (M.P.): It is the price at which the article is marked or tagged for sale.​

2) Discount: It is an amount which is subtracted from the marked price of an article before buying it.

For eg: 25% discount means a deduction of 25% in the marked price of the article.​

Subject |Maths

Ananya Goyal

Calculating Discount

Subject | Maths

Ananya Goyal

Sales Tax / VAT / GST​

Sales tax is the tax le​vied on the sales made by a shopkeeper. When we buy things or eat in restaurants, then we pay sales tax in addition to the price of the item or food we eat. This sales tax is charged by government on the selling price of an item.

NOTE: Sales tax is same as VAT and GST or you can say that ​VAT and GST were earlier known as Sales Tax.

Let us do one question and clear our concept more effectively.​

Subject | Maths

Ananya​ Goyal

Question ​Of VAT

Subject | Maths

Ananya Goyal

Multiple Choice

On which of the following dsicount is calculated?

• S.P.

• C.P.

• M.P.

• None of these

Multiple Choice

On which figure VAT is calculated?

• S.P.

• C.P.

• M.P.

• None of these

Multiple Choice

A colour TV is available for Rs. 26880 inclusive of VAT. If the original cost of Rs. 24000, find the rate of VAT.

• 12%

• 22%

• 10%

• 20%

Multiple Choice

The sales tax rate is 8%. If Rahul bought a new car and paid a sales tax of Rs. 1920, what was the cost of the car before tax?

• Rs 20000

• Rs 2400

• Rs 24000

• Rs 2

Important terms

Subject | Maths

Ananya Goyal

Amount: The total money

paid back to the lender or by the bank consists of the principal amount and the interest. This

is called the amount and is usually denoted as A.

Interest: The extra money paid for the use of the borrowed money is called interest, usually denoted as I.

Principal: The money borrowed from someone or deposited in a bank is called principal, usually denoted as P.

Simple Interest

Subject |Maths

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Compound Interest

Subject |Maths

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​

​​n = no. of

years

Difference b/w S.I. and C.I.

Subject | Maths

Ananya Goyal

​PARAMETER

​SIMPLE INTEREST

​COMPOUND INTEREST

​DEFINITION

​It can be defined as the sum paid back for using the borrowed money, over a fixed period of time.

​It can be defined as when the sum principal amount exceeds the due date for payment along with the rate of interest, for a period of time.

​FORMULA

​RETURN AMOUNT

​Much lesser as compared to C.I.

Much higher​

Difference b/w S.I. and C.I.

Subject | Maths

Ananya Goyal

​PARAMETER

​SIMPLE INTEREST

​COMPOUND INTEREST

​PRINCIPAL

AMOUNT

It is constant​.

It keeps on varying during the entire borrowing period.

GROWTH​

It remains quite uniform.

​It increases quite rapidly.

INTEREST

CHARGED

The interest charged ​is for the principal amount.

The interest charged is​ for the principal and accumulated interest.

Conversion Period

Subject | Maths

Ananya Goyal

For eg. If interest is compounded quarterly, then there are 4 conversion periods in a year and the quarterly rate will be one-fourth of the annual rate.​

​The time period after which the interest is added to the principal to make a new principal is called the ​conversion period.

Applications Of C.I.

​We apply C.I. in the following situations:

1) To calculate the increase or decrease of population of a village or city at a particular rate.

2) To calculate the growth of germs or bacteria at a certain rate.

3) To calculate the depreciation (value of a vehicle/item/product being used over a certain period of time.)

Let's talk about depreciation a little more.​

​

Subject |Maths

Ananya Goyal

Depreciation

Subject |Maths

Ananya Goyal

Example of Depreciation​

Subject |Maths

Ananya Goyal

QUESTIONS

Factorisation

Multiple Choice

In how mnay years will the simple interest on Rs. 1600 at the rate of $$5\ \frac{1}{2}$$  be Rs. 484?

• $$2\ \frac{1}{2}\ years$$  

• $$4\ \frac{1}{2}\ years$$  

• $$3\ \frac{1}{2\ }years$$  

• $$5\ \frac{1}{2}\ years$$  

Multiple Choice

Find the amount due and the compound interest on Rs. 6000 for two years at 9% per annum.

•  Rs. 6375.50, Rs. 1375.50

• Rs. 7125.40, Rs. 1125.40

• Rs. 7520.75, Rs. 1520.75    

• Rs. 7128.60, Rs.1128.60

Multiple Choice

If the amount on Rs. 6400 after two years is Rs. 7396, find the rate of compound interest.

• 5.5%

• 4.5%

• 6.5%

• 7.5%

Multiple Choice

What is the difference between simple and compound interests on a sum of Rs. 1000 at 10% per annum after 4 years?

•  Rs. 54.50 

• Rs. 75.50

• Rs.  64.10  

•  Rs. 60.60

Multiple Choice

What is the compound interest on Rs. 8000 at 20% per annum for 9 months compounded quarterly?

• Rs. 1251 

•  Rs. 1261 

•  Rs. 1271 

•  Rs. 1281 

Multiple Choice

The value of a machine in a factory depreciates by 20% every year. At the end of 3 years, the price comes down to Rs. 12800. What was the price of the machine 3 years back?

• Rs. 20,000

• Rs. 25,000

• Rs. 52,000

• Rs. 50,000

Multiple Choice

The price of a machine depreciates at 10% every year. If the present value of the machine be Rs. 100000, what will be its value after 3 years?

• Rs. 65,000

• Rs. 90,000

• Rs. 72,000

• Rs. 72,900

Multiple Choice

The interest paid by the banks, post offices, insurance companies is simple interest.

• True

• False

Multiple Choice

Compound interest is calculated on the amount of the previous year.

• True

• False

Multiple Choice

In compound interest, the principal remains constant for the whole period.

• True

• False

Multiple Choice

If the interest is compounded quarterly then there are 2 conversion periods in a year.

• True

• False

THANK YOU

Ananya Goyal​