Index NumbersMCQPYQ Dec. 21Question 3799 of 197
All Questions

The weighted averaged of price relatives of commodities, when the weights are equal to the value of commodities in the current year, yields _________ index number.

Options

AFisher's ideal
BLaspeyre's
CPaasche's
DMarshall-Edgeworth
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Correct Answer

✅ Option c — Paasche's

All Options:

  • AFisher's ideal
  • BLaspeyre's
  • CPaasche's
  • DMarshall-Edgeworth

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Detailed Solution & Explanation

When the weights are equal to the value of commodities in the **current year**, the weighted average of price relatives yields the **Paasche's** index number. Let's derive this for the base year values (w=p0q0\displaystyle w = p_0 q_0): Index=∑wR∑w=∑(p0q0)(p1p0)∑p0q0=∑p1q0∑p0q0=P01L\text{Index} = \frac{\sum w R}{\sum w} = \frac{\sum (p_0 q_0) \left(\frac{p_1}{p_0}\right)}{\sum p_0 q_0} = \frac{\sum p_1 q_0}{\sum p_0 q_0} = P_{01}^L which is Laspeyres. For current year values (w=p1q1\displaystyle w = p_1 q_1), taking the weighted harmonic mean of price relatives: Index=∑w∑wR=∑p1q1∑p1q1p1/p0=∑p1q1∑p0q1=P01P\text{Index} = \frac{\sum w}{\sum \frac{w}{R}} = \frac{\sum p_1 q_1}{\sum \frac{p_1 q_1}{p_1/p_0}} = \frac{\sum p_1 q_1}{\sum p_0 q_1} = P_{01}^P which is Paasche's. Hence, **Option C** 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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