Index NumbersMCQMTP Oct 21Question 3907 of 197
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From the following data for the 5\displaystyle 5 groups combined: Group Weights Index no Food 35 425 cloth 15 235 Power & Fuel 20 215 Rent & Rates 8 115 Miscellaneous 22 150. The general Index number is

Options

A370\displaystyle 370
B269.2\displaystyle 269.2
C268.5\displaystyle 268.5
D272.5\displaystyle 272.5
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Correct Answer

✅ Option b — 269.2\displaystyle 269.2

All Options:

  • A370\displaystyle 370
  • B269.2\displaystyle 269.2
  • C268.5\displaystyle 268.5
  • D272.5\displaystyle 272.5

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Detailed Solution & Explanation

To find the general index number, we compute the weighted arithmetic mean of the group index numbers: General Index=∑IW∑W\text{General Index} = \frac{\sum I W}{\sum W} Let's list the groups, weights (W\displaystyle W), and indices (I\displaystyle I): - Food: W=35,I=425  ⟹  IW=35×425=14875\displaystyle W = 35, I = 425 \implies I W = 35 \times 425 = 14875 - Cloth: W=15,I=235  ⟹  IW=15×235=3525\displaystyle W = 15, I = 235 \implies I W = 15 \times 235 = 3525 - Power & Fuel: W=20,I=215  ⟹  IW=20×215=4300\displaystyle W = 20, I = 215 \implies I W = 20 \times 215 = 4300 - Rent & Rates: W=8,I=115  ⟹  IW=8×115=920\displaystyle W = 8, I = 115 \implies I W = 8 \times 115 = 920 - Miscellaneous: W=22,I=150  ⟹  IW=22×150=3300\displaystyle W = 22, I = 150 \implies I W = 22 \times 150 = 3300 1. **Sum of Weights (∑W\displaystyle \sum W)**: ∑W=35+15+20+8+22=100\sum W = 35 + 15 + 20 + 8 + 22 = 100 2. **Sum of products (∑IW\displaystyle \sum I W)**: ∑IW=14875+3525+4300+920+3300=26920\sum I W = 14875 + 3525 + 4300 + 920 + 3300 = 26920 3. **Calculate General Index**: General Index=26920100=269.2\text{General Index} = \frac{26920}{100} = 269.2 Hence, **Option B** is the correct answer.

About This Chapter: Index Numbers

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Construction of Index Numbers, Time Series

This chapter covers Construction of Index Numbers, Time Series and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

Key Concepts to Understand

Index Number

A statistical device for measuring changes in the magnitude of a group of related variables (like prices or production) over time.

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More Questions from Index Numbers

In price index, when a new commodity is required to be added, which of the following index is used?

Fisher's ideal formula for calculating index number satisfies the ________

Shifted Price Index = Original Price IndexPrice Index of the year on which it has to be shifted×100\displaystyle \frac{\text{Original Price Index}}{\text{Price Index of the year on which it has to be shifted}} \times 100

If Laspeyres's Index Number is 250 and Paasche's Index Number is 160, then Fisher's Index number is

If ∑P0q0=240\displaystyle \sum P_0q_0 = 240, ∑P1q0=480\displaystyle \sum P_1q_0 = 480, ∑P0q1=600\displaystyle \sum P_0q_1 = 600 and ∑P1q1=192\displaystyle \sum P_1q_1 = 192, then Laspeyres's Index Number is

If ΣPnqn=249\displaystyle \Sigma P_n q_n = 249, ΣP0q0=150\displaystyle \Sigma P_0 q_0 = 150, ΣPnq0=145\displaystyle \Sigma P_n q_0 = 145 and Paasche's Index Number = 150, then Fisher's Ideal Price Index Number is

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