Name:- Ajay Rao and Name:- Ajay Rao and Raghunandan AgroyaRaghunandan Agroya

Roll. No.:- 3 and 12Roll. No.:- 3 and 12 Class:- 8Class:- 8thth ‘B’ ‘B’ House:- Dahlias and DaffodilsHouse:- Dahlias and Daffodils Teacher:- Mane SirTeacher:- Mane Sir

Introduction

This ppt consists information This ppt consists information about ratios, percentage, about ratios, percentage, discount, simple and compound discount, simple and compound interest, and amount. It has some interest, and amount. It has some problems and their solutions. problems and their solutions. This ppt contains some important This ppt contains some important formulas. formulas.

INDEXSr. No. Contents Slide No.1. Ratio & Percentage 4 & 5

2. Percentage increase or decrease

12

3. Percentage Change 14

4. Discount Percentage 15

5. Formulas with Discount Given

17

6. Sales tax/VAT, Profit and Loss

18

7. Simple Interest and Compound Interest

21

8. Applications of Compound Interest Formula

26

9. Summary 28

Comparing Quantities

Recalling Ratios and Percentages We know, ratio means comparing two or more than two quantities.

A basket has two types of fruits, we can say 35 bananas and 7 cherries.

Then, the ratio of the number of cherries to the number of bananas= 7:35.

The comparison can be done by using fractions as, 7/35 = 1/5. The number of cherries are 1/5th the number of bananas. In terms of

ratio, this is 1:5, read as, “1 is to 5.

RATIO AND PERCENTAGE

* Percent # The word per cent symbolically written as %

means in every 100 or per hundred. # To change a percentage to a fraction, write it as

a fraction with a denominator 100 and simplify if possible. To change it to a decimal, change the fraction so obtained to a decimal.

# To change fractions and decimals to percentage, multiply by 100.

To study we have some examples

Q: a picnic is being planed in a school for class 7th. Girls are 60% of the total number of students and are 28 in number.

The picnic site is 55km 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.

Can you tell. 1:} The ratio of the number of girls to the number of

boys of 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 22Km from the

school, what percent of the total distance of 55Km is this? What percent of the distance is left to be covered?

Solution 1 To find the ratio of girls and boys. Ashima and john come with the

following answers. They needed to know the number of

boys and also the total number of students.

So, the number of boys = 30 – 18 =12 Hence the ratio of the number of girls

to the number of boys is 18 : 12 is written as 3:2 and read as 3 is to 2

2:} To find the cost per person. Transporting charge = distance both ways X rate = Rs {55 X 2} X 12 = Rs 110 X 12 = Rs 1320 total expenses = Refreshment charge + transporting charge = Rs 4280 + Rs 1320 = Rs 5600total number of persons = 18girls +12boys +2

teacher = 32 personsAshima and john then used unitary method to find

the cost per head. For 32 persons, amount spend would be Rs 5600

The amount spend for 1 persons = Rs 5600 = Rs 175 32

3} The distance of the place where the first stop was made = 22 Km.

To find the percentage of distance:

22 = 22 X 100 = 40%55 55 100

Out of 55 km, 22km are traveled

Out of one km, 22 km are traveled 55

Examples to Understand

Find the ratio of the following. 1.Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour.

2. 5 m to10 km. 3. 75 paisa to Rs. 3.

Note: While finding the ratio of two quantities, the

quantities must be in the same unit.

Solutions

1. Ratio = Speed of cycle

Speed of scooter = 15 = 1 Ans- 1 : 2 30 2 2. Ratio = 5m_________ 10km = 10000m = 5__ = _1__ Ans- 1 : 2000 10000 2000 3. Ratio = __ 75p_____ Rs. 3 = 300p = 75 = 1 Ans- 1 : 4 300 4

# Percentage increase or decrease # To increase a quantity by a percentage,

find the percentage of the quantity and add it to the original quantity.

# To decrease a quantity by a percentage, find the percentage of the quantity and subtract it from the original quantity.

We often come across such information in our daily life as:-

1) 25% off on marked prices. 2) 10% hike in the price of petrol.

Example Price of a car was Rs. 3,27,000 before 2 years, it has

increased 10% this year, what is the price now ?Solution:- Given, Price of a car before 2 years = 327000. We know that, Increased price = 10% of 327000 = 10 X 327000 100 = Rs. 32700 The present price = Old price + Increased amount = 327000 + 32700 = Rs. 359700.

Ans- The price of car now is Rs. 3,59,700.

Percentage change = {Actual change x 100} Original a. # Gain% = {Gain x 100} C. P. # Loss% = {Loss x 100} C. P. # S. P. = {100 + Gain%} x C. P. 100 # S. P.= { 100-Loss% } x C. P. 100 # C. P.= { 100__} x S. P. 100+gain% # C. P.= {…..100……}x S. P. 100- Loss%

Percentage ChangePercentage Change

Discount percentage A ratio is an expression that compares quantities relative to

each other.When we compare two quantities in relation to each other, such a comparison is mathematically expressed as a ratio.Percent means ‘per hundred’ or out of hundred.Percentage is another way of comparing ratios that compares to hundred.

A change in a quantity can be positive, which means an increase, or negative, which means a decrease. Such a change can be measured by an increase percent or a decrease percent.Percentage Change (Increase/Decrease)

 

A discount is a price reduction offered on the marked price.

Discounts are offered by shopkeepers to attract customers to buy goods and thereby increase sales.

Discount = Marked price (MP) – Sale price (SP)

A discount is, in fact, a percentage decrease, because the amount of change or discount is compared with the initial price or marked price.

Formulas with Discount Given Rate of Discount = Discount X 100 Marked Price S. P. = M. P. X { 100 – Discount% } 100 M. P. = __100 X S. P.__ 100 – Discount%

Sales Tax/VAT, Profit and Loss Sales tax is charged by the government on the selling

price of an item and is included in the bill amount.Sales tax has been replaced by a new tax called Value Added Tax (VAT).Normally, VAT is included in the price of items like groceries.

Profit and loss depend on cost price and selling price. If cost price is less than selling price, there is a profit. Profit is calculated by subtracting cost price from selling price.Profit = SP – CP

If cost price is greater than selling price, then there is a loss. Loss is calculated by subtracting selling price from cost price.Loss = CP – SP.

Examples The cost of a pair of shoes at a shop was Rs. 550.

The sales tax charged was 4%. Find the bill amount.Solution:- Given, S. P. = Rs. 550. We know that, Sales tax = 4% of 550 = 4 X 550 100 = Rs. 22 Therefore, Bill amount = S. P. + Sales tax = 550 + 22 = Rs. 572.

Ans- The bill amount is Rs. 572.

Ramesh purchased one LCD for Rs. 12,000 including a tax of 10%. Find the price of the LCD before VAT was added.

Solution:- Let the price of LCD before adding VAT be Rs. y. Given that, y + 10% of y = 12000 y + 10 X y = 12000 100 y + y = 12000 10 11y = 12000 10 y = 12000 X 10 11 y = Rs. 10909

Ans- The price of LCD before adding VAT is Rs. 10909.

Interest is the extra money that a bank gives you for saving or depositing your money with them. Similarly, when you borrow money, you pay interest.

With Simple interest, the interest is calculated on the same amount of money in each time period, and, therefore, the interest t earned in each time period is the same.

On the other hand, compound interest is calculated on the principal plus the interest for the previous period. The principal amount  increases with every time period, as the interest payable is added to the principal. This means interest is not only earned on the principal, but also on the interest of the previous time periods.

So we can say that the compound interest calculated is more than the simple interest on the same amount of money deposited.

When interest is compounded, the total amount is calculated using the formula, A=P(1+ R) n.

100

Simple and Compound Interest

Interest is generally calculated on a yearly basis. Sometimes, it can be compounded more than once within a year. It can be compounded half yearly, which means twice a year, or quarterly, which means four times a year.The period for which interest is calculated is called the conversion period. At the end of the conversion period, the interest is added to the principal to get the new principal.

Simple interest = Principal x Rate x Time Period 100 Amount = Simple Interest + Principal Compound interest = Amount – Principal n Amount = P { 1+ R } 100

Examples Find the compound interest for Rs. 5000 at the rate of 10% per

annum for 3 years compounded annually.Solution:- Given, P = 5000 R = 10% p. a. N = 3 years We know, n A = P { 1 + R } 100 3 = 5000 { 1 + 10 } 100 = 5000 x 11 x 11 x 11 10 x 10 x 10 = 6655

Compound interest = Amount – Principal = 6655 - 5000 = Rs. 1655.

Ans- The compound interest is Rs. 1655.

What amount is to be repaid on a loan of Rs. 12000 for 1 year at 10% per annum compounded half yearly?

Solution:- Given, P = Rs. 12000 R = 10% p.a. N = 1 year As interest is compounded half yearly, N = 1 x 2 = 2 R = half of 10% = 5% half yearly We know that, n A = P { 1 + R } 100 2 = 12000 { 1 + 5 } 100 = 12000 x 21 x 21 20 x 20 = Rs. 13230

Ans- The amount to be repaid is Rs. 13230.

Applications of Compound Interest Formula

There are some situations where we could use the formula for calculation of amount in compound interest. Here are a few:-

Increase (or decrease) in population. The growth of a bacteria if the rate of

growth is known. The value of an item, if its price increases

or decreases in the intermediate years.

Examples In a Laboratory, the count of bacteria in a certain

experiment was increasing at the rate of 2.5% per hour. Find the bacteria at the end of 2 hours if the count was initially 5,06,000.

Solution:- Given, No. of bacteria at present = 5,06,000 Rate of increase = 2.5% We know that, No. of bacteria after 2 hours 2 = 506000 { 1 + 2.5 } 100 = 506000 x 41 x 41 40 x 40 = 531616

Ans- There will be approximately 531616 bacteria after 2 hours.

Summary Discount is a reduction given on marked price.Discount is a reduction given on marked price. Discount = Marked price – Sale price.Discount = Marked price – Sale price. Discount can be calculated when discount percentage is given.Discount can be calculated when discount percentage is given. Discount = Discount% of Marked price. Discount = Discount% of Marked price. Additional expenses made after buying an article are included in the cost Additional expenses made after buying an article are included in the cost

price and are known as overhead expenses.price and are known as overhead expenses. C. P. = Buying price + Overhead expenses.C. P. = Buying price + Overhead expenses. Sales tax is charged on the sale of an item by the government and is Sales tax is charged on the sale of an item by the government and is

added to the Bill Amount.added to the Bill Amount. Sales tax = Tax% of Bill Amount.Sales tax = Tax% of Bill Amount. Compound interest is the interest calculated on the previous year’s Compound interest is the interest calculated on the previous year’s

amount (A= P + I ).amount (A= P + I ). 1) Amount when interest is compounded annually1) Amount when interest is compounded annually nn = P { 1 + = P { 1 + R R } } 100100 2) Amount when interest is compounded half yearly2) Amount when interest is compounded half yearly 2n [ 2n [ RR is half yearly rate and ] is half yearly rate and ] = P { 1 + = P { 1 + R R } 2} 2 200200 [ 2n = number of ‘half years’ ][ 2n = number of ‘half years’ ]

References

Ncert class 8 textbook.Ncert class 8 textbook. www.learnnext.comwww.learnnext.com Class 7 state syllabus Maths textbook.Class 7 state syllabus Maths textbook. www.excellup.comwww.excellup.com