Index NumbersMCQPYQ May 18Question 3779 of 197
All Questions

Circular test is satisfied by

Options

ALaspeyre's Index Number
BPaasche's Index Number
CThe simple geometric mean of price relatives and the weighted aggregative with fixed weights
DNone of these
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — The simple geometric mean of price relatives and the weighted aggregative with fixed weights

All Options:

  • ALaspeyre's Index Number
  • BPaasche's Index Number
  • CThe simple geometric mean of price relatives and the weighted aggregative with fixed weights
  • DNone of these

Ad

Detailed Solution & Explanation

The **Circular Test** requires that the index formula allows for base shifting easily, such that: P01×P12×P20=1P_{01} \times P_{12} \times P_{20} = 1 Let's analyze the methods that satisfy this: 1. **Simple Geometric Mean of Price Relatives**: Pab=(∏i=1npb,ipa,i)1nP_{ab} = \left(\prod_{i=1}^n \frac{p_{b,i}}{p_{a,i}}\right)^{\frac{1}{n}} P01×P12×P20=(∏i=1np1,ip0,i)1n×(∏i=1np2,ip1,i)1n×(∏i=1np0,ip2,i)1n=1P_{01} \times P_{12} \times P_{20} = \left(\prod_{i=1}^n \frac{p_{1,i}}{p_{0,i}}\right)^{\frac{1}{n}} \times \left(\prod_{i=1}^n \frac{p_{2,i}}{p_{1,i}}\right)^{\frac{1}{n}} \times \left(\prod_{i=1}^n \frac{p_{0,i}}{p_{2,i}}\right)^{\frac{1}{n}} = 1 Thus, simple GM of price relatives satisfies the test. 2. **Weighted Aggregative Index with Fixed Weights**: Pab=∑pbw∑pawP_{ab} = \frac{\sum p_b w}{\sum p_a w} P01×P12×P20=(∑p1w∑p0w)×(∑p2w∑p1w)×(∑p0w∑p2w)=1P_{01} \times P_{12} \times P_{20} = \left(\frac{\sum p_1 w}{\sum p_0 w}\right) \times \left(\frac{\sum p_2 w}{\sum p_1 w}\right) \times \left(\frac{\sum p_0 w}{\sum p_2 w}\right) = 1 Thus, the weighted aggregative index with fixed weights also satisfies the test. Standard weighted indexes with variable weights (like Laspeyres, Paasche, Fisher) do not satisfy this test. 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.

Related Comparison Tables

Cardinal vs Ordinal Utility: Measuring Satisfaction

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

Ready to Master Index Numbers?

Practice all 197 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free