Chapter – I
1
RATIOS
&
BASIC ALGEBRA
Dr.Karthik Mohandoss
303203 - MATHEMATICS OF FINANCE
2
RATIO
Dr.Karthik Mohandoss
RATIO
A ratio is a way of comparing two or more quantities. If
Dr.Karthik Mohandoss
we have five red balls and three green balls, we say that
the ratio of red balls to green balls is 5 to 3.often this is
abbreviated 5:3.If in addition we have two blue balls, we
can express the ratio of red to green to blue as 5:3:2.
3
Example 1
Determine the ratio of 1 hour to 25 minutes.
Since 1 hour contains 60 minutes,
Dr.Karthik Mohandoss
we can write the ratio as ,
60:25
12:5
2.4:1
4
Example 2
Dr.Karthik Mohandoss
Suppose that $80,000 is to be allocated for advertising,
research, and investment in the ratio 8:5:3. How much
money will be spent allocated for each?
Solution :
Since 8+5+3 =16,
we divide $80,000 in to 16 parts of $ 5,000
(80,000 /16 =5,000).
5
Advertising gets 8 parts,
Then 5,000 * 8 = $40,000.
Dr.Karthik Mohandoss
Research gets 5 parts,
Then 5,000 * 5 = $25,000.
Investment gets 3 parts,
Then 5,000 * 3= $15,000.
Finally the sum of allocation is equal to $80,000.
($40,000+ $25,000+ $15,000)
6
Solved Problems
Reduce the ratios
250:75
Solution :
1.
Dr.Karthik Mohandoss
That Implies 250/75 = 10/3
(divided by 25)
So the reduced ratio is 10:3.
69:15
Solution :
That Implies 69/15 = 23/5
2.
(divided by 3)
So the reduced ratio is 23:5.
7
Dr.Karthik Mohandoss
3. A business spends $180,000 on advertising,
$120,000 on research and development, and
$150,000 on office rent. Find the ratio between
these expenses?
Solution :
$180,000:$150,000:$120,000 =18:15:12
(Divided by 10,000)
=6:5:4
(Divided by 3)
8
4. A $14,000 grant is to be divided between Harvard and Yale universities in
the Ratio 4:3. How much money should each university receive.
Solution :
Dr.Karthik Mohandoss
As the ratio is 4:3 we add both the ratio
i.e. 4+3 = 7
So we now divide $14,000 in to 7 parts
i.e. $14,000 / 7 = $2000
That denote Harvard gets 4 parts i.e $8,000 and Yale gets 3 parts $6000.
9
5. On an investment of OMR 50,000 Mr.Kamran receives OMR
65,000 after one year. If Mr.Kamran invested OMR 80,000 in the
same venture, how much should he be receiving?
Solution:
50/65=80/X
50X=65*80
(CROSS MULTIPLY)
THAT GIVES YOU
Dr.Karthik Mohandoss
50:65=80:X
50X=5,200
X=5,200/50
X=104
SO Mr. Kamran will receive OMR 104,000.
10
11
Dr.Karthik Mohandoss
BASIC ALGEBRA
In algebra. Symbols are called variable, are used to represent
numbers whose values are unknown. This enables us to work
with them even though we don’t yet know what their values
For example:
Dr.Karthik Mohandoss
are.
If p represents the price, in OMR, of a commodity, and we
wish to increase its price by 3OMR,its new price is represented
as p +3
12
The cost of manufacturing a computer is c OMR. what is the
cost of manufacturing 10 computers.
becomes 10c.here the we have to note that 10c is same as
Dr.Karthik Mohandoss
We multiply the cost of one computer by 10.hence the cost
10*c. In algebra, if symbol is omitted ,multiplication is
assumed.
13
EXAMPLE :
1. Abdhulla orders three T.V sets leaves a OMR 50 deposit. If
Solution
3x-50 = 1225
3x=1275 (add 50 to both the sides)
Dr.Karthik Mohandoss
the balance due is OMR 1,225,how much is each television set.
X=1275/3
Then each T.V. cost OMR 425
14
2. Walter orders eight chairs for his dinning-room table. He
leaves a OMR 75 deposit. if the balance due is
Solution
8x-75 = 845
8x=920 (add 75 to both the sides)
Dr.Karthik Mohandoss
OMR 845, how much is each chair cost.
X=920/8
Then each chair cost OMR 115
15
3. Ali ordered five DVD players and Two T.V sets for a total cost
of OMR 1,260. Each T.V set cost OMR 390. How much is one
Let d represent the cst of one DVD. Since two T.V sets cost OMR
780(2*390),we have the equation
5d + 780 = 1260
Dr.Karthik Mohandoss
DVD player?
Now we have to solve for d to get the cost of one DVD player
5d=1260-780
d=480/5
D=96
16
4. Samuel goes to the store and buys five video tapes and seven rolls of
films. He pays OMR 30.95.if each video tape costs OMR 3.25,how
much is a roll of film?
Let r be the cost of one film roll. Since five video tapes cost
16.25 (3.25 *5),we have the equation
7r+16.25 = 30.95
7r = 30.95 – 16.25
Dr.Karthik Mohandoss
Solution
7r = 14.7
r = 14.7/7
R = 2.1
Therefore the cost of one film roll is OMR 2.1
17
THANK YOU
18
Dr.Karthik Mohandoss