Index NumbersMCQPYQ June 19Question 3877 of 197
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The prices and quantities of 3 commodities in base and current years are as follows: | | P0\displaystyle P_0 | q0\displaystyle q_0 | P1\displaystyle P_1 | q1\displaystyle q_1 | |---|---|---|---|---| | T2 | 12 | 14 | 20 | 20 | | T0 | 8 | 10 | 20 | 30 | | T8 | 10 | 30 | 10 | 10 | The Laspeyre price index is

Options

A118.13\displaystyle 118.13
B107.14\displaystyle 107.14
C120.10\displaystyle 120.10
DNone of these
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Correct Answer

✅ Option d — None of these

All Options:

  • A118.13\displaystyle 118.13
  • B107.14\displaystyle 107.14
  • C120.10\displaystyle 120.10
  • DNone of these

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Detailed Solution & Explanation

Let's compute the sums of products of prices and quantities from the given table: - For Commodity T2: P0=12,q0=14,P1=20,q1=20\displaystyle P_0 = 12, q_0 = 14, P_1 = 20, q_1 = 20 - For Commodity T0: P0=8,q0=10,P1=20,q1=30\displaystyle P_0 = 8, q_0 = 10, P_1 = 20, q_1 = 30 - For Commodity T8: P0=10,q0=30,P1=10,q1=10\displaystyle P_0 = 10, q_0 = 30, P_1 = 10, q_1 = 10 1. **Calculate ∑P0q0\displaystyle \sum P_0q_0**: ∑P0q0=(12×14)+(8×10)+(10×30)=168+80+300=548\sum P_0q_0 = (12 \times 14) + (8 \times 10) + (10 \times 30) = 168 + 80 + 300 = 548 2. **Calculate ∑P1q0\displaystyle \sum P_1q_0**: ∑P1q0=(20×14)+(20×10)+(10×30)=280+200+300=780\sum P_1q_0 = (20 \times 14) + (20 \times 10) + (10 \times 30) = 280 + 200 + 300 = 780 3. **Calculate Laspeyres Price Index**: P01L=∑P1q0∑P0q0×100=780548×100≈142.34P_{01}^L = \frac{\sum P_1q_0}{\sum P_0q_0} \times 100 = \frac{780}{548} \times 100 \approx 142.34 Since the calculated index is 142.34\displaystyle 142.34, which is not in the options A, B, or C, it corresponds to None of these. 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.

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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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