METHODS AND TECHNIQUES ON BUSINESS DATA ANALYSIS

Notes 31 Pages

Bengaluru City University

Bachelor of Business Administration

Contributed by

Prajwal Hallale

NOTES ON
METHODS AND
TECHNIQUES ON
BUSINESS DATA
ANALYSIS
II SEM BCOM AND BBA

SMT DIVYASHREE D V and SRI VIJAY
MESIOM

Page 1
Ratios
A ratio is a simple mathematical term used for comparing two or more quantities that are
measured in the same units.

Ratios are the comparison of two quantities or more quantities (having the same units) that
we express as a fraction. The concept of equivalent fractions allows the ratios of different
physical quantities to be the same sometimes. Thus, a ratio is a general term independent
of a unit and we use it across multiple platforms.
Consider the following example : A shopkeeper sells mangoes for 50 rupees per kg and
buys them at a wholesale price of 30 rupees per kg. What is the ratio of his profit to the
cost price per kg?
Solution: For 1 kg of mangoes,
The profit = Selling Price – Cost Price
= 50 – 30
= 20 rupees

Then we write the ratio of his profit to the cost price per kg as : Profit per kg /Cost Price
per kg
=20/30
=2/3
This is the fractional form of the ratio formula. We can equivalently express it as 10/15
or any other equivalent fraction. But conventionally, we only use the reduced form of the
fraction. Notation-wise, we then say that the ratio of the shopkeeper’s profit to the cost
price per kg = 2 : 3

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Properties of Ratios
 We express a ratio only between two quantities of the same units. (rupees per kg in
the above example)
 We use the symbol ‘:’ to denote ratios.
 We call two ratios as equivalent if their corresponding fractions are equivalent.
 For ratios written as a : b, the first term i.e. a is known as the antecedent and the
second term i.e. b is known as the consequent.
 The order of the terms in ratios is very important i.e. the positions of antecedent and
consequent are not interchangeable.
 If more than one like quantities are expressed in a ratio format, the resultant is
termed as a Continued Ratios or a Compassion between the quantities. It can simply
be represented as a : b : c : d…
Compound Ratio Formula
When we compound/merge two or more ratios with each other through multiplication, the
result is simply a compound ratio.
Consider two known ratios a : b and c : d. Then the Compound Ratio of the two
mentioned ratios is ac : bd.
Duplicate ratio: If we compound a ratio a : b with itself once, it results in a Duplicate
Ratio, which we give as a
2
: b
2
.
Triplicate ratio: If we triplicate a ratio a : b with itself once, it results in a triplicate
Ratio, which we give as a
3
: b
3
.
Sub-Duplicate ratio of a : b as √a : √b. Similarly, you can also form Sub-Triplicate ratios
by taking a cube root and so on. These ratios don’t come straightaway under the category
of Compound Ratios but are analogous to the self-compounded ratios.
Inverse Ratio Formula
By taking the reciprocal of the fractional form of the given ratios, we get inverse ratios.
The inverse ratio of a : b = b : a. Another property of the inverse ratios which is simple to
understand is = Ratio × Its Inverse Ratio = 1
Commensurate Ratios
Page 3
Ratios whose antecedent and consequent both, are only integers, is a Commensurate
Ratios. For example, in the solved example that we solved above resulted in a
commensurate ratio 2:3. Instead of such a simple ratio, if we get something like 3:Π(pie)
or √2:5, then it is not a commensurate ratio.
NOTE: A ratio such as 0.75:2 may seem like commensurate ratios at first, but actually if
you just multiply its fractional form by 4, you’ll get the resultant ratio 3:8. This indeed is a
commensurate ratio. Thus, you have to be careful with some cases.
1: What number do we need to subtract from each of the terms in the ratio 19:31 to reduce
it to the ratio 1 : 4?
Solution: Let the required number be x. Writing the modified ratio (after subtracting x
from each of the terms in 19 : 31) in fractional form and expressing it equal to 1 : 4
19–x / 31–x=1 / 4
4×(19–x)=1×(31–x) Cross multiply
76–4x=31–x
45=3x
x=15
2: The ratio compounded of 4 : 9, the duplicate ratio of 3 : 4, the triplicate ratio of 2 : 3,
and 9 : 7 is ?
Solution: We need to compound four different ratios here –
 4 : 9
 3
2
: 4
2
= 9 : 16
 2
3
: 3
3
= 8 : 27
 9 : 7
By the definition of the compounded ratios, the final result would be –
4×9×8×9:9×16×27×7
Writing it in fractional form –
4×9×8×9 / 9×16×27×7
=2 / 21
Thus, the required ratio is 2 : 21.

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3: If Rs 782 is to be divided in the ratio 6 : 8 : 9, then what value would the first share
correspond to?
Solution: Consider a unit share to be equivalent to Rs x. Then the first share would be
equivalent to Rs 6x. The second share ⇒ 8x. The third share ⇒ 9x. By common sense, the
sum of all shares should be equal to the total amount. Thus –
6x+8x+9x=782
23x=782
x=34
Clearly then, the value of the first share ⇒ Rs 34*6 ⇒ Rs 204

Proportion

If we say that two ratios are equal then it is called Proportion.

We write it as a: b : : c: d or a: b = c: d.. And reads as “a is to b as c is to d”.

Example

1) If a man runs at a speed of 20 km in 2 hours then with the same speed would he be able
to cross 40 km in 4 hours?

Solution

Here the ratio of the distances given is 20/40 = 1/2 = 1: 2
And the ratio of the time taken by them is also 2/4 = 1/2 = 1: 2
Hence the four numbers are in proportion.
We can write them in proportion as 20: 40 : : 2: 4
And reads as “20 is to 40 as 2 is to 4”.

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Extreme Terms and Middle Terms of Proportion

The first and the fourth term in the proportion are called extreme terms and the second and
third terms are called the Middle or the Mean Terms.
In this statement of proportion, the four terms which we have written in order are called
the Respective Terms.
If the two ratios are not equal then these are not in proportion.

1: Check whether the terms 30,99,20,66 are in proportion or not.
Solution . To check the numbers are in proportion or not we have to equate the ratios.

As both the ratios are equal so the four terms are in proportion.
30: 99 :: 20: 66
We can check with the product of extremes and the product of means. In the
respective terms 30, 99, 20, 66
30 and 66 are the extremes 99 and 20 are the means.
To be in proportion the product of extremes must be equal to the product of means.
30 × 66 = 1980 99 × 20 = 1980
The product of extremes = product of means
Hence, these terms are in proportion.

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2: Find the ratio 30 cm to 4 m is proportion to 25 cm to 5 m or not.
Solution 2: As the unit is different so we have to convert them into the same unit.
4 m = 4 × 100 cm = 400 cm
The ratio of 30 cm to 400 cm is

5 m = 5 × 100 cm = 500 cm
Ratio of 25 cm to 500 cm is

Here the two ratios are not equal so these ratios are not in proportion.
3: 40 ≠ 1: 20

Unitary Method
If we find the value of one unit then calculate the value of the
required number of units then this method is called the Unitary method.
Example 1: If the cost of 3 books is 320 Rs. then what will be the cost of 6 books?

Solution 1
Cost of 3 books = Rs. 320
Cost of 1 book = 320/3 Rs.
Cost of 6 books = (320/3) × 6 = 640 Rs.
Hence, the cost of 6 books is Rs. 640.

2: If the cost of 20 toys is Rs. 4000 then how many toys can be purchased for Rs. 6000?
Solution 2
In Rs. 4000, the number of toys can be purchased = 20
In Rs. 1, the number of toys can be purchased = Rs. 20/4000
Therefore, in Rs. 6000, the number of toys can be purchased = (20/4000) × 6000 = 30
Hence, 30 toys can be purchased by Rs. 6000.

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Continued Proportions
Three quantities are said to be in continued proportion if a : b = b : c. In fractional form
ab=ac
Here, you can see that b
2
= ac. This is also known as the Cross Product Rule. We call b as
the mean proportional between a and c in this case. We can extend the concept of
continuous proportions for more than three quantities in the following way
ab=bc=cd=de…..
a : b = b : c = c : d = d : e ….
Properties of Proportions
1. Invertendo
a : b = c : d ⇔ b : a = d : c
2. Alternendo
a : b = c : d ⇔ a : c = b : d
3. Componendo
a : b = c : d ⇔ a + b : b = c + d : d
4. Dividendo
a : b = c : d ⇔ a – b : b = c – d : d
5. Componendo and Dividendo
a : b = c : d ⇔ a + b : a – b = c + d : c – d
6. Equality of Addendoes
a : b = c : d = e : f ….. = k (say)
Then any term of the form a + c + e ….. : b + d + f…, is known as an Addendo. And, all of
such ratios (Addendoes) are equal to the original ratio i.e.
a + c : b + d = a + e : b + f = a + c + e : b + d + f = …… = k

Page 8
Problems:
1: The numbers 14, 16, 35, 42 are not in proportion. The fourth term for which they will
be in proportion is?
Solution: Let the fourth term be x. By the definition of the ratios being in proportion –
14 / 16=35 / x
x=35×16 / 14
x=40
Clearly, the fourth term has to be equal to 40, not 42, for the numbers given to be in
proportion.
2: If x/4 = y/3 = z/2, then what would be the value of (5x + y – 2z)/3y?
Solution: Let us assume that the given ratios in the continued proportion are all equal to an
integer k. Then,
X / 4=y / 3=z / 2=k
Considering the ratios now one at a time, we get –
x=4k
y=3k
z=2k

Use these values to evaluate the required expression
=(5x+y–2z) / 3y
=(5×4k+3k–2×2k) / 3×3k
=19k / 9k
=19 / 9
3: A certain recipe calls for 3kgs of sugar for every 6 kgs of flour. If 60kgs of this sweet
has to be prepared, how much sugar is required?
Solution:: Let the quantity of sugar required be x kgs.
3 kgs of sugar added to 6 kgs of flour constitutes a total of 9 kgs of sweet.
3 kgs of sugar is present in 9 kgs of sweet. We need to find the quantity of sugar required
for 60 kgs of sweet. So the proportion looks like this.
3/9 = x/60
X= (3*60)/ 9
→ x=20.
Page 9
Therefore, 20 kgs of sugar is required for 60 kgs of sweet.
6: If a 60 ml of water contains 12% of chlorine, how much water must be added in order to
create a 8% chlorine solution?
Solution:
Let x ml of chlorine be present in water.
Then, 12/100 = x/60 → x = 7.2 ml
Therefore, 7.2 ml is present in 60 ml of water.
In order for this 7.2 ml to constitute 8% of the solution, we need to add extra water. Let
this be y ml.
Then, 8/100 = 7.2/y → y = 90 ml.
So in order to get a 8% chlorine solution, we need to add 90-60 = 30 ml of water.
INTEREST
SIMPLE INTEREST
In simple interest we will learn and identify about the terms like Principal, Time, Rate,
Amount, etc.
Suppose Ron has deposited 100/- in a bank. Ron goes to the bank to find out about his
deposited money. The manager of the bank informs Ron that 100 deposited in the bank
one year before has now become 110. Ron enquires how did 100 become 110 after one
year?
The manager told that when someone deposits money in a bank, we pay some extra money
on the deposited amount.
Here, the money borrowed (loan is the principal and the extra money to be paid is called
the interest.
The interest is only a fair payment for using another person’s money.
PRINCIPAL (P):
The money you deposit or put in the bank is called the PRINCIPAL.

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METHODS AND TECHNIQUES ON BUSINESS DATA ANALYSIS

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