comparing quantities class 8

2. 
Name:- Ajay Rao and Raghunandan Name:- Ajay Rao and Raghunandan
AgroyaAgroya

Roll. No.:- 3 and 12Roll. No.:- 3 and 12

Class:- 8Class:- 8
thth
‘B’ ‘B’

House:- Dahlias and DaffodilsHouse:- Dahlias and Daffodils

Teacher:- Mane SirTeacher:- Mane Sir

3. 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. This problems and their solutions. This
ppt contains some important ppt contains some important
formulas. formulas.

4. INDEX
Sr. 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

5. 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 1/5
th
the number of
bananas. In terms of ratio, this is 1:5, read as,
“1 is to 5.

6. 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.

7. To sTudy we have some examples
Q: a picnic is being planed in a school for class 7
th
. 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?

8. 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

9. 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 5600
total number of persons = 18girls +12boys +2 teacher
= 32 persons
Ashima 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

10. 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

11. 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.

12. 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

13. # 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.

14. 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.

15. 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

16. 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)

 

17. 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.

18. 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%

19. 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.

20. 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.

21. 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.

22. 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

23. 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.

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

25. 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.

26. 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.

27. 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.

28. 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.

29. 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 Additional expenses made after buying an article are included in
the cost price and are known as overhead expenses.the cost 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 Sales tax is charged on the sale of an item by the government
and is added to the Bill Amount.and is 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 Compound interest is the interest calculated on the previous
year’s amount (A= P + I ).year’s 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’ ]

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