Index NumbersMCQPYQ Jan. 21Question 3797 of 197
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When the prices for quantities consumed of all commodities are changing in the same ratio, then the index numbers due to Laspeyre's and Paasche's will be.

Options

AEqual
BUnequal
CReciprocal of Marshall Edge worth Index Number
DReciprocal of Fisher Index Number
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Correct Answer

✅ Option a — Equal

All Options:

  • AEqual
  • BUnequal
  • CReciprocal of Marshall Edge worth Index Number
  • DReciprocal of Fisher Index Number

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Detailed Solution & Explanation

When the prices for quantities consumed of all commodities change in the exact same ratio k\displaystyle k (i.e., p1i=kp0i\displaystyle p_{1i} = k p_{0i} for all commodities i\displaystyle i), let's evaluate Laspeyres and Paasche index numbers: 1. **Laspeyres Index (P01L\displaystyle P_{01}^L)**: P01L=∑p1q0∑p0q0×100=∑(kp0)q0∑p0q0×100=k×100P_{01}^L = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100 = \frac{\sum (k p_0) q_0}{\sum p_0 q_0} \times 100 = k \times 100 2. **Paasche Index (P01P\displaystyle P_{01}^P)**: P01P=∑p1q1∑p0q1×100=∑(kp0)q1∑p0q1×100=k×100P_{01}^P = \frac{\sum p_1 q_1}{\sum p_0 q_1} \times 100 = \frac{\sum (k p_0) q_1}{\sum p_0 q_1} \times 100 = k \times 100 Since both indices are equal to k×100\displaystyle k \times 100, they will be **equal**. Hence, **Option A** 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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