If sum P1 Q1 = 249 , sum P0 Q0 = 150 Paasche's Index Number = 150 and Dorbish and Bowley's Index Number = 145 , then the Fisher's Ideal Index Number is

Option b: 144.91. Solution: We are given: - Paasche's Index ( P ) = 150 - Dorbish-Bowley's Index ( B ) = 145 The Dorbish-Bowley index is the arithmetic mean of Laspeyres' ( L ) and Paasche's ( P ) indices: B = L + P/2 Substitute the given values to solve for L : 145 = L + 150/2 290 = L + 150 L = 140 Fisher's Ideal Index ( F ) is the geometric mean of Laspeyres' and Paasche's indices: F = sqrt(L × P) = sqrt(140 × 150) = sqrt(21000) ≈ 144.9137 This rounds to 144.91 . Hence, Option B is the correct answer.

If $\sum P_1 Q_1 = 249$, $\sum P_0 Q_0 = 150$ Paasche's Index Number $= 150$ and Dorbish and Bowley's Index Number $= 145$, then the Fisher's Ideal Index Number is

The correct answer is Option b: $144.91$. We are given: - Paasche's Index ($P$) = $150$ - Dorbish-Bowley's Index ($B$) = $145$ The Dorbish-Bowley index is the arithmetic mean of Laspeyres' ($L$) and Paasche's ($P$) indices: $$B = \frac{L + P}{2}$$ Substitute the given values to solve for $L$: $$145 = \frac{L + 150}{2} \implies 290 = L + 150 \implies L = 140$$ Fisher's Ideal Index ($F$) is the geometric mean of Laspeyres' and Paasche's indices: $$F = \sqrt{L \times P} = \sqrt{140 \times 150} = \sqrt{21000} \approx 144.9137$$ This rounds to $144.91$. Hence, **Option B** is the correct answer.

Index NumbersMCQMTP Dec 23 Series IIQuestion 3925 of 197

All Questions

If $\displaystyle \sum P_1 Q_1 = 249$ , $\displaystyle \sum P_0 Q_0 = 150$ Paasche's Index Number $\displaystyle = 150$ and Dorbish and Bowley's Index Number $\displaystyle = 145$ , then the Fisher's Ideal Index Number is

Options

\displaystyle 175

\displaystyle 144.91

\displaystyle 145.97

DNone of these

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — $\displaystyle 144.91$

All Options:

A $\displaystyle 175$
B $\displaystyle 144.91$
C $\displaystyle 145.97$
DNone of these

Detailed Solution & Explanation

We are given: - Paasche's Index (

\displaystyle P

) =

\displaystyle 150

- Dorbish-Bowley's Index (

\displaystyle B

) =

\displaystyle 145

The Dorbish-Bowley index is the arithmetic mean of Laspeyres' (

\displaystyle L

) and Paasche's (

\displaystyle P

) indices:

B = \frac{L + P}{2}

Substitute the given values to solve for

\displaystyle L

145 = \frac{L + 150}{2} \implies 290 = L + 150 \implies L = 140

Fisher's Ideal Index (

\displaystyle F

) is the geometric mean of Laspeyres' and Paasche's indices:

F = \sqrt{L \times P} = \sqrt{140 \times 150} = \sqrt{21000} \approx 144.9137

This rounds to

\displaystyle 144.91

. 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 ∑P1Q1=249\displaystyle \sum P_1 Q_1 = 249∑P1​Q1​=249, ∑P0Q0=150\displaystyle \sum P_0 Q_0 = 150∑P0​Q0​=150 Paasche's Index Number =150\displaystyle = 150=150 and Dorbish and Bowley's Index Number =145\displaystyle = 145=145, then the Fisher's Ideal Index Number is