Index NumbersMCQPYQ Jun 24Question 3893 of 197
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If the prices of all commodities in the base year are twice the values of the respective commodities in the current year, then the Fisher's ideal index number is equal to:

Options

A200\displaystyle 200
B50\displaystyle 50
C400\displaystyle 400
D25\displaystyle 25
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Correct Answer

✅ Option b — 50\displaystyle 50

All Options:

  • A200\displaystyle 200
  • B50\displaystyle 50
  • C400\displaystyle 400
  • D25\displaystyle 25

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Detailed Solution & Explanation

We are given: The prices of all commodities in the base year (P0\displaystyle P_0) are twice the prices in the current year (P1\displaystyle P_1): P0=2P1  ⟹  P1=0.5P0P_0 = 2 P_1 \implies P_1 = 0.5 P_0 Let's substitute this relation into the Laspeyres and Paasche index formulas: 1. **Laspeyres Price Index (P01L\displaystyle P_{01}^L)**: P01L=∑P1q0∑P0q0×100=∑(0.5P0)q0∑P0q0×100=0.5×100=50P_{01}^L = \frac{\sum P_1 q_0}{\sum P_0 q_0} \times 100 = \frac{\sum (0.5 P_0) q_0}{\sum P_0 q_0} \times 100 = 0.5 \times 100 = 50 2. **Paasche Price Index (P01P\displaystyle P_{01}^P)**: P01P=∑P1q1∑P0q1×100=∑(0.5P0)q1∑P0q1×100=0.5×100=50P_{01}^P = \frac{\sum P_1 q_1}{\sum P_0 q_1} \times 100 = \frac{\sum (0.5 P_0) q_1}{\sum P_0 q_1} \times 100 = 0.5 \times 100 = 50 3. **Fisher's Ideal Index (P01F\displaystyle P_{01}^F)**: P01F=P01L×P01P=50×50=50P_{01}^F = \sqrt{P_{01}^L \times P_{01}^P} = \sqrt{50 \times 50} = 50 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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