Index NumbersMCQMTP Mar 22Question 3913 of 197
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Find the Paasche's index number for prices from the followingCommodity | Base Year | Current Year| P | Q | P | QA | 1 | 6 | 3 | 5B | 3 | 5 | 8 | 5C | 4 | 8 | 10 | 6

Options

A261.36\displaystyle 261.36
B265.48\displaystyle 265.48
C274.32\displaystyle 274.32
D282\displaystyle 282
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Correct Answer

✅ Option a — 261.36\displaystyle 261.36

All Options:

  • A261.36\displaystyle 261.36
  • B265.48\displaystyle 265.48
  • C274.32\displaystyle 274.32
  • D282\displaystyle 282

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Detailed Solution & Explanation

Let's list the prices and quantities from the table: - Commodity A: P0=1,Q0=6,P1=3,Q1=5\displaystyle P_0=1, Q_0=6, P_1=3, Q_1=5 - Commodity B: P0=3,Q0=5,P1=8,Q1=5\displaystyle P_0=3, Q_0=5, P_1=8, Q_1=5 - Commodity C: P0=4,Q0=8,P1=10,Q1=6\displaystyle P_0=4, Q_0=8, P_1=10, Q_1=6 We compute the sums of products for Paasche's Index: 1. **Calculate ∑P0Q1\displaystyle \sum P_0 Q_1**: ∑P0Q1=(1×5)+(3×5)+(4×6)=5+15+24=44\sum P_0 Q_1 = (1 \times 5) + (3 \times 5) + (4 \times 6) = 5 + 15 + 24 = 44 2. **Calculate ∑P1Q1\displaystyle \sum P_1 Q_1**: ∑P1Q1=(3×5)+(8×5)+(10×6)=15+40+60=115\sum P_1 Q_1 = (3 \times 5) + (8 \times 5) + (10 \times 6) = 15 + 40 + 60 = 115 3. **Calculate Paasche's Price Index**: P01P=∑P1Q1∑P0Q1×100=11544×100≈261.36P_{01}^P = \frac{\sum P_1 Q_1}{\sum P_0 Q_1} \times 100 = \frac{115}{44} \times 100 \approx 261.36 This matches Option A. 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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More Questions from Index Numbers

In price index, when a new commodity is required to be added, which of the following index is used?

Fisher's ideal formula for calculating index number satisfies the ________

Shifted Price Index = Original Price IndexPrice Index of the year on which it has to be shifted×100\displaystyle \frac{\text{Original Price Index}}{\text{Price Index of the year on which it has to be shifted}} \times 100

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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