Index NumbersMCQMTP Nov 19Question 3897 of 197
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The Paasches and Fishers index numbers are 169\displaystyle 169 and 156\displaystyle 156 respectively, then Laspeyre's Index number is

Options

A144\displaystyle 144
B152\displaystyle 152
C148\displaystyle 148
D151.5\displaystyle 151.5
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Correct Answer

✅ Option a — 144\displaystyle 144

All Options:

  • A144\displaystyle 144
  • B152\displaystyle 152
  • C148\displaystyle 148
  • D151.5\displaystyle 151.5

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Detailed Solution & Explanation

We are given: - Paasche's Index (P\displaystyle P) = 169\displaystyle 169 - Fisher's Index (F\displaystyle F) = 156\displaystyle 156 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 values: 1562=L×169  ⟹  24336=169L156^2 = L \times 169 \implies 24336 = 169 L L=24336169=144L = \frac{24336}{169} = 144 Thus, Laspeyres' index is 144\displaystyle 144. 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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Fisher's ideal formula for calculating index number satisfies the ________

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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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