Optimization and numeric techniques.pptx

Example-1
Directions (1 -5):
5/6/2024
Faculty Name: Dr. Kunti Mishra Optimization & Numerical Techniques
(AAS0404) Unit V 1
Data Interpretation (CO5)

1. What is the average amount of interest per
year which the company had to pay during this
period?
A. Rs. 32.43 lakhs
B. Rs. 33.72 lakhs
C. Rs. 34.18 lakhs
D. Rs. 36.66 lakhs
Sol: Average amount of interest paid by the
Company during the given period
=
Rs. [૛૜.૝ + ૜૛.૞ + ૝૚.૟ + ૜૟.૝ + ૝ૢ.૝૞ ]
5
lakhs
= Rs. 36.66 lakhs.
5/6/2024
(AAS0404) Unit V
2

2. The total amount of bonus paid by the company
during the given period is approximately what
percent of the total amount of salary paid during
this period?
A. 0.1%
B. 0.5%
C. 1%
D. 1.25%
Explanation:
Required percentage =
[ (૜.૙૙ + ૛.૞૛ + ૜.ૡ૝ + ૜.૟ૡ + ૜.ૢ૟) x 100 ] %
(૛ૡૡ + ૜૝૛ + ૜૛૝ + ૜૜૟ + ૝૛૙)
= 1%.
5/6/2024
(AAS0404) Unit V
3

3. Total expenditure on all these items in 1998 was
approximately what percent of the total expenditure
in 2002?
A. 62%
B. 66%
C. 69%
D. 71%
Explanation:
Required percentage =
[(૛ૡૡ + ૜૝૛ + ૜૛૝ + ૜૜૟ + ૝૛૙)x 100 ] %
(૝૛૙ + ૚૝૛ + ૜.ૢ૟ + ૝ૢ.૝ + ૢૡ)
= 69.45 %.
5/6/2024
(AAS0404) Unit V
4

4. The total expenditure of the company over these
items during the year 2000 is?
A. Rs. 544.44 lakhs
B. Rs. 501.11 lakhs
C. Rs. 446.46 lakhs
D. Rs. 478.87 lakhs
Explanation:
Total expenditure of the Company during 2000
= Rs. (324 + 101 + 3.84 + 41.6 + 74) lakhs
= Rs. 544.44 lakhs.
5/6/2024
(AAS0404) Unit V 5

5. The ratio between the total expenditure on Taxes
for all the years and the total expenditure on Fuel
and Transport for all the years respectively is
approximately?
A. 4:7
B. 10:13
C. 15:18
D. 5:8
Explanation:
Required ratio=
(ૡ૜ + ૚૙ૡ + ૠ૝ + ૡૡ + ૢૡ)
(ૢૡ + ૚૚૛ + ૚૙૚ + ૚૜૜ + ૚૝૛)
=
10
13
5/6/2024
(AAS0404) Unit V
6

Example:2
Directions (1-5): The following pie-chart shows the
number of students who failed in different subjects
in an examination, Examine the chart and answer the
following questions. The total number of students
who have failed in 500.
5/6/2024 Faculty Name: Dr. Kunti Mishra Optimization & Numerical Techniques
(AAS0404) Unit V
7
Mathematics,
30%,
Science,
32%,
Language ,
36%
Other, 2%,
Mathematics Science Language Other

1. The number of students failed in science is less
than the number of students failed in all other
subjects by:
A. 170
B. 140
C. 180
D. 160
Explanation:
Required=
500(68−32)
100
= 180
5/6/2024
(AAS0404) Unit V
8

2. The central angle of the sector for the students
who have failed in mathematics is:
A. 30°
B. 100°
C. 105.2°
D. 108°
Explanation:
Required=
30
100
× 360
=108
5/6/2024
(AAS0404) Unit V 9

3. Total number of students who did not qualify in
Mathematics and Language and Science is:
A. 460
B. 490
C. 480
D. 470
Explanation:
Required=
98
100
× 500
= 490
5/6/2024
(AAS0404) Unit V 10

4. Number of students who failed in mathematics is
less then the students who did not qualify in
languages by:
A. 20
B. 40
C. 30
D. 50
Required=
500(36−30)
100
= 30
5/6/2024
Faculty Name: Dr. Kunti Mishra Optimization & Numerical
Techniques (AAS0404) Unit V 11

5. The percentage of students who have failed in mathematics
and language is:
A. 65.5%
B. 60%
C. 66%
D. 62%
Explanation:
Required percentage=(36 + 30) = 66%
5/6/2024
(AAS0404) Unit V 12

Number System
Permutation & Combination
Probability
Function
Data Interpretation
5/6/2024
(AAS0404) Unit V 13
Recap(CO2)

Syllogism (CO5)
Introduction:
The questions which are asked in this section contain
two or more statements and these statements are
followed by two or more conclusions. You have to find
out which of the conclusions logically follow from
the given statements. The statements have to be taken
true even if they seem to be at variance from the
commonly known facts.
For such questions, you can take the help of Venn
Diagrams. On the basis of the given statements, you
should draw all the possible diagrams, and then
derive the solution from each of these diagrams
separately. Finally, the answer common to the all the
diagrams is taken.
5/6/2024
Faculty Name: Dr. Kunti Mishra Optimization & Numerical Techniques (AAS0404)
Unit V
14

Syllogism (CO5)
Example 1:
Statements:
1.All dogs are asses.
2.All asses are bulls.
Conclusions:
1.Some dogs are not bulls.
2.Some bulls are dogs.
3.All bulls are dogs.
4.All dogs are bulls.
5/6/2024
(AAS0404) Unit V 15

Syllogism (CO5)
Solution:
On the basis of both statements, the following one
diagram is possible.
From the diagram it is clear that (2) and (4)
conclusions logically follow.
5/6/2024
Unit V 16

Syllogism (CO5)
Example:2
Statements:
Some actors are singers.
All the singers are dancers.
Conclusions:
1.Some actors are dancers.
2.No singer is actor.
Then
A.Only (1) conclusion follows
B.Only (2) conclusion follows
C.Either (1) or (2) follows
D.Neither (1) nor (2) follows
5/6/2024
(AAS0404) Unit V
17

Syllogism (CO5)
Sol:
Only 1 follows
5/6/2024
Unit V
18

Syllogism (CO5)
Example:3
Statements:
No door is dog.
All the dogs are cats.
Conclusions:
1.No door is cat.
2.No cat is door.
3.Some cats are dogs.
4.All the cats are dogs.
Then
A.Only (2) and (4)
B.Only (1) and (3)
C.Only (3) and (4)
D.Only (3)
5/6/2024
(AAS0404) Unit V 19

Syllogism (CO5)
Sol:
Only 3 follows
5/6/2024
(AAS0404) Unit V 20

Syllogism (CO5)
Example-4
Statements: All the locks are keys. All the keys are
bats. Some watches are bats.
Conclusions:
1. Some bats are locks.
2.Some watches are keys.
3.All the keys are locks.
Then
A. Only (1) and (2)
B. Only (1)
C. Only (2)
D. Only (1) and Only (3)
5/6/2024
(AAS0404) Unit V 21

Syllogism (CO5)
Sol:
5/6/2024
(AAS0404) Unit V 22

1.Statements:
Some ants are parrots.
All the parrots are apples
Conclusions:
1.All the apples are parrots.
2.Some ants are apples.
Then
A.Only (1) conclusion follows
B.Only (2) conclusion follows
C.Neither (1) nor (2) follows
D.Both (1) and (2) follow
5/6/2024
(AAS0404) Unit V 23
Syllogism (CO5)

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