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HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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Mathematics and Statistics
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Calculate Walsh’s Price Index Number for the following data.

Commodity Base year Current year
  Price
p0
Quantity
q0
Price
p1
Quantity
q1
I 8 30 12 25
II 10 42 20 16
[13] Index Numbers
Chapter: [13] Index Numbers
Concept: undefined >> undefined

Solve the following problem :

Calculate Laspeyre’s and Paasche’s Price Index Number for the following data.

Commodity Base Year Current Year
  Price
P0
Quantity
q0
Price
p1
Quantity
q1
I 8 30 12 25
II 10 42 20 16
[13] Index Numbers
Chapter: [13] Index Numbers
Concept: undefined >> undefined

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Find x if Laspeyre’s Price Index Number is same as Paasche’s Price Index Number for the following data

Commodity Base Year Current Year
  Price
p0
Quantity
q0
Price
p1
Quantity
q1
A 3 x 2 5
B 4 6 3 5
[13] Index Numbers
Chapter: [13] Index Numbers
Concept: undefined >> undefined

Solve the following problem:

If find x is Walsh’s Price Index Number is 150 for the following data

Commodity Base Year Current Year
  Price
p0
Quantity
q0
Price
p1
Quantity
q1
A 5 3 10 3
B x 4 16 9
C 15 5 23 5
D 10 2 26 8
[13] Index Numbers
Chapter: [13] Index Numbers
Concept: undefined >> undefined

Solve the following problem :

Find x if Paasche’s Price Index Number is 140 for the following data.

Commodity Base Year Current Year
  Price
p0
Quantity
q0
Price
p1
Quantity
q1
A 20 8 40 7
B 50 10 60 10
C 40 15 60 x
D 12 15 15 15
[13] Index Numbers
Chapter: [13] Index Numbers
Concept: undefined >> undefined

Solve the following problem :

Given that Laspeyre’s and Paasche’s Price Index Numbers are 25 and 16 respectively, find Dorbish-Bowley’s and Fisher’s Price Index Number.

[13] Index Numbers
Chapter: [13] Index Numbers
Concept: undefined >> undefined

If Laspeyre’s and Dorbish’s Price Index Numbers are 150.2 and 152.8 respectively, find Paasche’s Price Index Number.

[13] Index Numbers
Chapter: [13] Index Numbers
Concept: undefined >> undefined

Solve the following problem :

If `sum"p_"0"q"_0 = 120, sum "p"_0"q"_1 = 160, sum "p"_1"q"_1 = 140, and sum "p"_1"q"+0` = 200, find Laspeyre’s, Paasche’s Dorbish-Bowley’s and Marshall Edgeworth’s Price Index Number.

[13] Index Numbers
Chapter: [13] Index Numbers
Concept: undefined >> undefined

Solve the following problem :

Given that `sum "p"_0"q"_0 = 130, sum "p"_1"q"_1 = 140, sum "p"_0"q"_1 = 160, and sum "p"_1"q"_0 = 200`, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and Marshall-Edgeworth’s Price Index Numbers.

[13] Index Numbers
Chapter: [13] Index Numbers
Concept: undefined >> undefined

Solve the following problem :

Given that `sum "p"_1"q"_1 = 300, sum "p"_0"q"_1 = 320, sum "p"_0"q"_0` = 120, and Marshall- Edgeworth’s Price Index Number is 120, find `sum"p"_1"q"_0` and Paasche’s Price Index Number.

[13] Index Numbers
Chapter: [13] Index Numbers
Concept: undefined >> undefined

A job production unit has four jobs A, B, C, D which can be manufactured on each of the four machines P, Q, R and S. The processing cost of each job for each machine is given in the following table:

Jobs Machines
(Processing Cost in ₹)
P Q R S
A 31 25 33 29
B 25 24 23 21
C 19 21 23 24
D 38 36 34 40

Find the optimal assignment to minimize the total processing cost.

[15] Assignment Problem and Sequencing
Chapter: [15] Assignment Problem and Sequencing
Concept: undefined >> undefined

Five wagons are available at stations 1, 2, 3, 4, and 5. These are required at 5 stations I, II, III, IV, and V. The mileage between various stations are given in the table below. How should the wagons be transported so as to minimize the mileage covered?

  I II III IV V
1 10 5 9 18 11
2 13 9 6 12 14
3 3 2 4 4 5
4 18 9 12 17 15
5 11 6 14 19 10
[15] Assignment Problem and Sequencing
Chapter: [15] Assignment Problem and Sequencing
Concept: undefined >> undefined

Five different machines can do any of the five required jobs, with different profits resulting from each assignment as shown below:

Job Machines (Profit in ₹)
A B C D E
1 30 37 40 28 40
2 40 24 27 21 36
3 40 32 33 30 35
4 25 38 40 36 36
5 29 62 41 34 39

Find the optimal assignment schedule.

[15] Assignment Problem and Sequencing
Chapter: [15] Assignment Problem and Sequencing
Concept: undefined >> undefined

The assignment problem is said to be unbalance if ______

[15] Assignment Problem and Sequencing
Chapter: [15] Assignment Problem and Sequencing
Concept: undefined >> undefined

The assignment problem is said to be balanced if ______.

[15] Assignment Problem and Sequencing
Chapter: [15] Assignment Problem and Sequencing
Concept: undefined >> undefined

Choose the correct alternative :

The assignment problem is said to be balanced if it is a ______.

[15] Assignment Problem and Sequencing
Chapter: [15] Assignment Problem and Sequencing
Concept: undefined >> undefined

Choose the correct alternative :

In an assignment problem if number of rows is greater than number of columns then

[15] Assignment Problem and Sequencing
Chapter: [15] Assignment Problem and Sequencing
Concept: undefined >> undefined

The objective of an assignment problem is to assign ______. 

[15] Assignment Problem and Sequencing
Chapter: [15] Assignment Problem and Sequencing
Concept: undefined >> undefined

Fill in the blank :

When an assignment problem has more than one solution, then it is _______ optimal solution.

[15] Assignment Problem and Sequencing
Chapter: [15] Assignment Problem and Sequencing
Concept: undefined >> undefined

Fill in the blank :

An _______ is a special type of linear programming problem.

[15] Assignment Problem and Sequencing
Chapter: [15] Assignment Problem and Sequencing
Concept: undefined >> undefined
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