Index NumbersPYQ May 25Question 4095 of 197
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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

Options

A75
B126.9
C120.62
D171
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Correct Answer

✅ Option c — 120.62

All Options:

  • A75
  • B126.9
  • C120.62
  • D171

Detailed Solution & Explanation

Fisher's Ideal Index (F\displaystyle F) is the geometric mean of Laspeyres' Index (L\displaystyle L) and Paasche's Index (P\displaystyle P):
F=L×PF = \sqrt{L \times P}
First, let us calculate Laspeyres' Price Index (L\displaystyle L):
L=ΣPnq0ΣP0q0×100L = \frac{\Sigma P_n q_0}{\Sigma P_0 q_0} \times 100 Substituting the given values, ΣPnq0=145\displaystyle \Sigma P_n q_0 = 145 and ΣP0q0=150\displaystyle \Sigma P_0 q_0 = 150:
L=145150×100=2930×100≈96.67L = \frac{145}{150} \times 100 = \frac{29}{30} \times 100 \approx 96.67 (If we use the unrounded fraction L=96.6667\displaystyle L = 96.6667, or if we round to 97\displaystyle 97):
- Using L≈97\displaystyle L \approx 97:
F=97×150=14550≈120.62F = \sqrt{97 \times 150} = \sqrt{14550} \approx 120.62 - Using L=96.6667\displaystyle L = 96.6667:
F=96.6667×150=14500≈120.42F = \sqrt{96.6667 \times 150} = \sqrt{14500} \approx 120.42 Given the options, 120.62\displaystyle 120.62 is the intended answer obtained by rounding the Laspeyres' Index to 97 before calculating the geometric mean.

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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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

From the following data, find out an Index number for 2022 taking 2021 as base (using simple aggregative method): A (80, 120), B (220, 200), C (300, 400).

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