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Chapters
1.2: Matrices
1.3: Differentiation
1.4: Applications of Derivatives
1.5: Integration
1.6: Definite Integration
1.7: Application of Definite Integration
1.8: Differential Equation and Applications
2.1: Commission, Brokerage and Discount
2.2: Insurance and Annuity
2.3: Linear Regression
2.4: Time Series
▶ 2.5: Index Numbers
2.6: Linear Programming
2.7: Assignment Problem and Sequencing
2.8: Probability Distributions
![SCERT Maharashtra solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC chapter 2.5 - Index Numbers - Shaalaa.com](/images/mathematics-and-statistics-commerce-english-12-standard-hsc_6:5f2b1b2038084cf381bfa42c826a928c.jpg "SCERT Maharashtra solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC chapter 2.5 - Index Numbers")
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Solutions for Chapter 2.5: Index Numbers
Below listed, you can find solutions for Chapter 2.5 of Maharashtra State Board SCERT Maharashtra for Mathematics and Statistics (Commerce) [English] 12 Standard HSC.
SCERT Maharashtra solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC 2.5 Index Numbers Q.1
MCQ [ Mark]
Choose the correct alternative:
Price Index Number by using Weighted Aggregate Method is given by
`(sum"p"_1"q")/(sum"p"_0"q") xx 100`
`sum"p"_1"w" xx 100`
`(sum"p"_1"w")/(sum"p"_0"w") xx 100`
`(sum"p"_0"w")/(sum"p"_1"w") xx 100`
Choose the correct alternative:
The formula P01 = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100` is for
Laspeyre’s Price Index Number
Paasche’s Price Index Number
Fisher’s Price Index Number
Walsh’s Price Index Number
Choose the correct alternative:
Dorbish–Bowley’s Price Index Number is
P01(L) + P01(P)
P01(L) – P01(P)
`("P"_(01)("L") + "P"_(01)("P"))/2 xx 100`
`("P"_(01)("L") + "P"_(01)("P"))/2`
Choose the correct alternative:
`(sum"p"_1"q"_1"w")/(sum"p"_0"q"_0"w") xx 100` gives
Value Index Number by Simple Aggregate method
Value Index Number by Weighted Aggregate method
Cost of Living Index Number
Laspeyre’s Index Number
Choose the correct alternative:
Walsh's Price Index Number is given by
`(sum"p"_0 sqrt("p"_0"p"_1))/(sum"q"_1 sqrt("p"_0"p"_1)) xx 100`
`(sum"p"_0 sqrt("q"_0"q"_1))/(sum"p"_1 sqrt("q"_0"q"_1)) xx 100`
`(sum"q"_1 sqrt("p"_0"p"_1))/(sum"q"_0 sqrt("p"_0"p"_1)) xx 100`
`(sum"p"_1 sqrt("q"_0"q"_1))/(sum"p"_0 sqrt("q"_0"q"_1)) xx 100`
Quantity Index Number by Simple Aggregate Method is given by ______.
`sum(q_1)/(q_0) xx 100`
`sum(q_0)/(q_1) xx 100`
`(sumq_1)/(sumq_0) xx 100`
`(sumq_0)/(sumq_1) xx 100`
Choose the correct alternative:
Fisher’s Price Index Number is
`sqrt("P"_(01)("L") xx "P"_(01)("P"))`
P01(L) × P01(P)
`sqrt("P"_(01)("L") xx "P"_(01)("P")) xx 100`
`sqrt("P"_(01)("L") + "P"_(01)("P"))`
Choose the correct alternative:
The Cost of Living Index Number using Weighted Relative Method is given by
`(sum"IW")/(sum"W") xx 100`
`(sum"IW")/(sum"W")`
`(sum"W")/(sum"IW") xx 100`
`(sum"W")/(sum"IW")`
Choose the correct alternative:
The Cost of Living Index Number by Aggregate Expenditure Method is same as
Fisher’s Price Index Number
Laspeyre’s Price Index Number
Paasche’s Price Index Number
Dorbish-Bowley’s Price Index Number
SCERT Maharashtra solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC 2.5 Index Numbers Q.2
Fill in the blanks [1 Mark]
Price Index Number by Simple Aggregate Method is given by ______
Value Index Number by Simple Aggregate Method is given by ______
Fisher's Price Index Number is given by ______.
Marshall-Edgeworth's Price Index Number is given by ______
The Cost of Living Index Number by Aggregate Expenditure Method is given by ______
The average of Laspeyre’s and Paasche’s Price Index Numbers is called ______ Price Index Number
Quantity Index Number by Weighted Aggregate Method is given by ______.
Price Index Number by Weighted Aggregate Method is given by ______
SCERT Maharashtra solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC 2.5 Index Numbers Q.3
[1 Mark]
State whether the following statement is True or False:
Walsh’s Price Index Number is given by `(sum"p"_1sqrt("q"_0"q"_1))/(sum"p"_0sqrt("q"_0"q"_1)) xx 100`
True
False
State whether the following statement is True or False:
The three types of Index numbers are
i. Price Index Number
ii. Quantity Index Number
iii. Value Index Number
True
False
State whether the following statement is True or False:
For Cost of Living Index Number CLI =`(sum"IW")/(sum"W")`, where I = `("P"_0)/("P"_1) xx 100` and w = p0q0
True
False
State whether the following statement is True or False:
Purchasing power of money = `1/"Cost of Living Index Number"`
True
False
State whether the following statement is True or False:
`sum("q"_1)/("q"_0) xx 100` is the Quantity Index Number by Simple Aggregate Method
True
False
State whether the following statement is True or False:
`(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100` is Paasche’s Price Index Number
True
False
State whether the following statement is True or False:
`(sum"p"_0sqrt("q"_0 + "q"_1))/(sum"p"_1sqrt("q"_0 + "q"_1)) xx 100` is Marshall-Edgeworth Price Index Number
True
False
State whether the following statement is True or False:
`[sqrt((sum"p"_1"q"_1)/(sum"p"_0"q"_1)) + (sumsqrt("q"_0"q"_1))/(sum("p"_0 + "p"_1))] xx 100` is Fisher’s Price Index Number.
True
False
State whether the following statement is True or False:
`sum ("P"_1"q"_1)/("p"_0"q"_0) xx 100` is the Value Index Number by Simple Aggregate Method
True
False
SCERT Maharashtra solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC 2.5 Index Numbers Q.4
Solve the following problems [4 Marks]
Find Price Index Number using Simple Aggregate method by taking 2005 as base year.
| Commodity | P | Q | R | S | T |
| Price in 2005 (in ₹) | 10 | 25 | 14 | 20 | 30 |
| Price in 2015 (in ₹) | 32 | 40 | 20 | 45 | 70 |
Find Quantity Index Number using Simple Aggregate method
| Commodity | A | B | C | D | E |
| Base year Quantity | 170 | 150 | 100 | 195 | 205 |
| Current year Quantity | 90 | 70 | 75 | 150 | 95 |
Calculate Value Index Number for the following using Simple Aggregate Method
| Commodity | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| A | 30 | 13 | 40 | 15 |
| B | 40 | 15 | 70 | 20 |
| C | 10 | 12 | 60 | 22 |
| D | 50 | 10 | 90 | 18 |
| E | 20 | 14 | 100 | 16 |
Calculate Quantity Index Number using Simple Aggregate method
| Commodity | I | II | III | IV | V |
| Base year Quantity | 140 | 120 | 100 | 200 | 225 |
| Current year Quantity | 100 | 80 | 70 | 150 | 185 |
Find Price Index Number using Simple Aggregate method by taking 2000 as base year
| Commodity | Price (in ₹) for year 2000 |
Price (in ₹) for year 2007 |
| Watch | 900 | 1,475 |
| Shoes | 1,760 | 2,300 |
| Sunglasses | 60 | 1,040 |
| Mobile | 4,500 | 8,500 |
Find x if the Price Index Number by Simple Aggregate Method is 125
| Commodity | P | Q | R | S | T |
| Base Year Price (in ₹) | 10 | 8 | 12 | 24 | 18 |
| Current Year Price (in ₹) | 14 | 10 | x | 28 | 22 |
Find values x and y if the Price Index Number by Simple Aggregate Method by taking 2001 as base year is 120, given `sum"p"_1` = 300.
| Commodity | A | B | C | D |
| Price (in ₹) in 2001 | 90 | x | 90 | 30 |
| Price (in ₹) in 2004 | 95 | 60 | y | 35 |
Find x from following data if the Value Index Number is 200.
| Commodity | Base Year | Current Year | ||
| Prive | Quantity | Price | Quantity | |
| A | 10 | 10 | 20 | 10 |
| B | 8 | 20 | 22 | 15 |
| C | 2 | x | 8 | 10 |
| D | 9 | 10 | 16 | 10 |
| E | 5 | 6 | 3 | 10 |
Calculate
a) Laspeyre’s
b) Passche’s
c) Dorbish-Bowley’s Price Index Numbers for following data.
| Commodity | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| A | 10 | 9 | 50 | 8 |
| B | 20 | 5 | 60 | 4 |
| C | 30 | 7 | 70 | 3 |
| D | 40 | 8 | 80 | 2 |
Calculate Marshall-Edgeworth Price Index Number for following.
| Commodity | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| A | 8 | 20 | 11 | 15 |
| B | 7 | 10 | 12 | 10 |
| C | 3 | 30 | 5 | 25 |
| D | 2 | 50 | 4 | 35 |
Calculate Walsh’s price Index Number for the following data.
| Commodity | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| I | 10 | 12 | 40 | 3 |
| II | 20 | 2 | 25 | 8 |
| III | 30 | 3 | 50 | 27 |
| IV | 60 | 9 | 90 | 36 |
If P01(L) = 40 and P01(P) = 90, find P01(D-B) and P01(F).
If Laspeyre’s and Paasche’s Price Index Numbers are 50 and 72 respectively, find Dorbish-Bowley’s and Fisher’s Price Index Numbers
Given P01(M-E) = 120, `sum"p"_1"q"_1` = 300, `sum"p"_0"q"_0` = 120, `sum"p"_0"q"_1` = 320, Find P01(L)
Find the missing price if Laspeyre’s and Paasche’s Price Index Numbers are equal for following data.
| Commodity | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| A | 1 | 10 | 2 | 5 |
| B | 1 | 5 | – | 12 |
If `sum"p"_0"q"_0` = 150, `sum"p"_0"q"_1` = 250, `sum"p"_1"q"_1` = 375 and P01(L) = 140. Find P01(M-E)
Calculate the Cost of Living Index Number for the following data.
| Group | Base Year | Current Year | |
| Price | Quantity | Price | |
| Food | 40 | 5 | 20 |
| Clothing | 30 | 10 | 35 |
| Fuel and Lighting | 20 | 17 | 10 |
| House Rent | 60 | 22 | 10 |
| Miscellaneous | 70 | 25 | 8 |
Calculate the Cost of Living Index by Family Budget method in following example where W are wages of base year and I are current year price relatives.
| Group | Food | Clothing | Fuel and Lighting |
House Rent |
Miscellaneous |
| I | 150 | 140 | 100 | 120 | 200 |
| W | 4 | 3 | 3 | 4 | 6 |
Find the missing wage if the Cost of Living Index for the following data is 150.
| Group | Food | Clothing | Fuel and Lighting |
House Rent |
Miscellaneous |
| I | 200 | 150 | 140 | 100 | 120 |
| W | 6 | 4 | x | 3 | 4 |
The Cost of Living Index Numbers for years 2003 and 2008 are 150 and 200 respectively. A person earned ₹ 18,000 per month in year 2003. What should be his earning per month in year 2008, so as to maintain same standard of living as 2003?
SCERT Maharashtra solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC 2.5 Index Numbers Q.5
Activity [4 Marks]
Given the following table, find Walsh’s Price Index Number by completing the activity.
| Commodity | p0 | q0 | p1 | q1 | q0q1 | `sqrt("q"_0"q"_1)` | p0`sqrt("q"_0"q"_1)` | p1`sqrt("q"_0"q"_1)` |
| I | 20 | 9 | 30 | 4 | 36 | `square` | `square` | 180 |
| II | 10 | 5 | 50 | 5 | `square` | 5 | 50 | `square` |
| III | 40 | 8 | 10 | 2 | 16 | `square` | 160 | `square` |
| IV | 30 | 4 | 20 | 1 | `square` | 2 | `square` | 40 |
| Total | – | – | – | – | 390 | `square` |
Walsh’s price Index Number is
P01(W) = `square/(sum"p"_0sqrt("q"_0"q"_1)) xx 100`
= `510/square xx 100`
= `square`
Given the following table, find the Cost of living Index Number using Aggregate Expenditure Method by completing the activity.
| Group | p0 | q0 | p1 | p0q0 | p1q0 |
| A | 23 | 4 | 25 | `square` | 100 |
| B | 15 | 5 | 20 | 75 | `square` |
| C | 5 | 9 | 8 | `square` | 72 |
| D | 12 | 5 | 18 | 60 | `square` |
| E | 8 | 6 | 13 | `square` | 78 |
| Total | – | – | – | 320 | `square` |
Therefore, Cost of Living Index using Aggregate Expenditure method is
CLI = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx square`
= `square/square xx 100`
= `square`
Solutions for 2.5: Index Numbers
SCERT Maharashtra solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC chapter 2.5 - Index Numbers
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Concepts covered in Mathematics and Statistics (Commerce) [English] 12 Standard HSC chapter 2.5 Index Numbers are Index Numbers, Types of Index Numbers, Index Numbers - Terminology and Notation, Construction of Index Numbers, Simple Aggregate Method, Weighted Aggregate Method, Cost of Living Index Number, Method of Constructing Cost of Living Index Numbers - Aggregative Expenditure Method, Method of Constructing Cost of Living Index Numbers - Family Budget Method, Uses of Cost of Living Index Number.
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