Index NumbersMCQPYQ Nov. 20Question 3880 of 197
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In Laspeyre's index number is 110 and Fisher's ideal index number is 109. Then Paasche's index number is

Options

A118\displaystyle 118
B110\displaystyle 110
C109\displaystyle 109
D108\displaystyle 108
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Correct Answer

✅ Option d — 108\displaystyle 108

All Options:

  • A118\displaystyle 118
  • B110\displaystyle 110
  • C109\displaystyle 109
  • D108\displaystyle 108

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Detailed Solution & Explanation

We are given: - Laspeyres' Index (L\displaystyle L) = 110\displaystyle 110 - Fisher's Ideal Index (F\displaystyle F) = 109\displaystyle 109 Fisher's index is the geometric mean of Laspeyres' (L\displaystyle L) and Paasche's (P\displaystyle P) indices: F=L×P  ⟹  F2=L×PF = \sqrt{L \times P} \implies F^2 = L \times P Substitute the given values into the equation: 1092=110×P  ⟹  11881=110×P109^2 = 110 \times P \implies 11881 = 110 \times P P=11881110≈108.01P = \frac{11881}{110} \approx 108.01 This rounds to 108\displaystyle 108. Hence, **Option D** 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

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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