If Fisher's index number is 160 and Paasche's index number is 140 , then Laspeyre's index number is

Option b: 182.85. Solution: We are given: - Fisher's Index ( F ) = 160 - Paasche's Index ( P ) = 140 Fisher's index is the geometric mean of Laspeyres' ( L ) and Paasche's ( P ) indices: F = sqrt(L × P) F2 = L × P Substitute the values: 1602 = L × 140 25600 = 140 L L = 25600/140 ≈ 182.857 This corresponds to Option B. Hence, Option B is the correct answer.

If Fisher's index number is $160$ and Paasche's index number is $140$, then Laspeyre's index number is

The correct answer is Option b: $182.85$. We are given: - Fisher's Index ($F$) = $160$ - Paasche's Index ($P$) = $140$ Fisher's index is the geometric mean of Laspeyres' ($L$) and Paasche's ($P$) indices: $$F = \sqrt{L \times P} \implies F^2 = L \times P$$ Substitute the values: $$160^2 = L \times 140 \implies 25600 = 140 L$$ $$L = \frac{25600}{140} \approx 182.857$$ This corresponds to Option B. Hence, **Option B** is the correct answer.

Index NumbersMCQPYQ Jun 23Question 3889 of 197

All Questions

If Fisher's index number is $\displaystyle 160$ and Paasche's index number is $\displaystyle 140$ , then Laspeyre's index number is

Options

\displaystyle 147.77

\displaystyle 182.85

\displaystyle 183.35

\displaystyle 146.25

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Correct Answer

✅ Option b — $\displaystyle 182.85$

All Options:

A $\displaystyle 147.77$
B $\displaystyle 182.85$
C $\displaystyle 183.35$
D $\displaystyle 146.25$

Detailed Solution & Explanation

We are given: - Fisher's Index (

\displaystyle F

) =

\displaystyle 160

- Paasche's Index (

\displaystyle P

) =

\displaystyle 140

Fisher's index is the geometric mean of Laspeyres' (

\displaystyle L

) and Paasche's (

\displaystyle P

) indices:

F = \sqrt{L \times P} \implies F^2 = L \times P

Substitute the values:

160^2 = L \times 140 \implies 25600 = 140 L

L = \frac{25600}{140} \approx 182.857

This corresponds to Option B. Hence, **Option B** 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 Fisher's index number is 160\displaystyle 160160 and Paasche's index number is 140\displaystyle 140140, then Laspeyre's index number is