Index Numbers Class 11 OP Malhotra Exe-30A ISC Maths Ch-30 Solutions. In this article you would learn about Simple Aggregate Method and Price Relative. Step by step solutions of latest textbook has been given as latest syllabus. Visit official Website CISCE for detail information about ISC Board Class-11 Mathematics.
Index Numbers Class 11 OP Malhotra Exe-30A ISC Maths Solutions Ch-30
| Board | ISC |
| Publications | S Chand |
| Subject | Maths |
| Class | 11th |
| Chapter-30 | Index Numbers |
| Writer | O.P. Malhotra |
| Exe-30(A) | Simple Aggregate Method and Price Relative. |
Simple Aggregate Method and Price Relative.
Index Numbers Class 11 OP Malhotra Exe-30A ISC Maths Ch-30 Solutions.
Using the simple aggregate method, calculate the price index number from the following data :
Que-1:
Sol: We construct the table of values is given as under :
Using simple aggregate method,
P01 = {ΣP1 / ΣP0} × 100 = (176/107) × 100 = 164.486
Que-2:
Sol: We construct the table is as under:
∴ required price index number = P01
= ΣP1 / ΣP0 × 100 = (410/350) × 100 = 117.143
Que-3:
Sol: We construct the table is as under:
Using simple aggregate method
Price index = P01 = ΣP1 / ΣP0 × 100 = (300/250) × 100 = 120
Que-4: Using 2005 as base year, the index numbers for the price of a commodity in 2006 and 2007 are 118 and 125. Calculate the index numbers for 2005 and 2007 if 2006 is taken as the base year.
Sol: Let prices in year 2005, 2006 and 2007 are P0, P1 and PP2 respectively.
Given (P1/P0) × 100 = 118 …(1)
and (P2/P0) × 100 = 125 …(2)
Thus index number for 2005 with 2006 as base year = (P0/P1) × 100 = (100/118) × 100
= 84.745
Index number for 2007 with 2006 as base year
(P2/P1) × 100 = {(P2/P0) × 100} / {(P1/P0) × 100}
= (125/118) × 100 = 105.93
Compute a price index for the following by using price relative method.
Que-5: Compute a price index for the following by using price relative method.
Sol: We construct the table as under :
Using price relative method,
price index = [Σ{(P1/P0)×100}] / n
= 796.67/5 = 159.334
Que-6:
Sol: We construct the table as under:
using price relative method, price index = Σ((P1/P0)×100)) / n = 630.53/4 = 157.6325
Que-7: The index number for the following data for the year 2008 , taking 2004 as base year was found to be 116. The simple aggregate method was used for calculation. Find the numerical value of x and y if the sum of the prices in the year 2008 is ₹ 203.
Sol: We construct the following table given as under:
Since sum of prices in the year 2011 = ΣP1 = 150 + y
⇒ 203 = 150 + y
⇒ y = 53
Thus Index number for year 2011 = ΣP1 / ΣP0 × 100
⇒ 116 = ((150+y)/(135+x)) × 100
⇒ 116 = {(203×100)/(135+x)}
⇒ 135 + x = {(203×100)/116} = 175
⇒ x = 175 – 135 = 40
Que-8: Construct index numbers by the simple average of relative method for 1990 and 1991 with 1989 as the base year.
Sol: We construct the table of values is under:
Que-9: Construct the index number for 1991 taking 1990 as the base year from the following data by simple average of price relative method.
Sol: We construct the table as under :
Then by simple average of price relative method,
price index = ΣP1 / P0 × 100 = 611.591/5 = 122.3182
Que-10: Construct index number from the following data for 1991 and 1992 taking 1990 as base by using the method of simple average of price relatives :
Sol: We construct a table of values is given as under:
By method of simple average of price relatives, we have
price Index for 1991 = [Σ(P1/P0)×100]/n = 512.5/4 = 128.125
and price index for 1992 = [Σ(P2/P0)×100]/n = 456/4 = 114
Que-11: The following data relate to the price of rice in different years.
Find out price relatives
(i) taking 1988 as base;
(ii) 1992 as base ;
(iii) taking average of 1988,1989 and 1990 as base.
Sol: We construct table of values is given as under:
(iii) base year value P0 = (6+7+7)/3 = 20/3
Que-12: Compute a price index for the following by (i) simple aggregate and (ii) average of price relative method.
Sol: We construct the table of values is given as under :
(i) By simple aggregate method, price index = ΣP1 / ΣP0 × 100 = (205/175) × 100 = 117.143
(ii) By average of price method, we have, price index = Σ((P1/P0)×100)/n = 737.5/6 = 122.92
Que-13: Construct an index for 1998 taking 1997 as base by Average of Relatives.
Sol: We construct the table of values is given as under :
Then by average of relative method, Price index = Σ((P1/P0)×100)/n = 611.591/5 = 122.32
Que-14: Construct the consumer price index number for 1990 taking 1989 as the base year and using simple average of price relative method for the following data :
Sol: We construct the table of values is given as under :
Using simple average of price relatives method
required index number = P01 = (1/N) Σ((P1/P0)×100) × 380 = 95
–: End of Index Number Class 11 OP Malhotra Exe-30A ISC Maths Ch-30 Solutions. :–
Return to :- OP Malhotra ISC Class-11 S Chand Publication Maths Solutions
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