Index NumbersMCQPYQ Jun 23Question 3887 of 197
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Consider the data: Year Base year Current year Commodities Price Quantity Price Quantity A 10 5 20 2 B 15 4 25 8 C 20 2 30 4 D 25 3 40 4. Laspeyre's index is

Options

A166.04\displaystyle 166.04
B166.40\displaystyle 166.40
C164.04\displaystyle 164.04
D164.4\displaystyle 164.4
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Correct Answer

✅ Option a — 166.04\displaystyle 166.04

All Options:

  • A166.04\displaystyle 166.04
  • B166.40\displaystyle 166.40
  • C164.04\displaystyle 164.04
  • D164.4\displaystyle 164.4

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Detailed Solution & Explanation

Let's compute the sums of products of prices and quantities: - Commodity A: P0=10,q0=5,P1=20,q1=2\displaystyle P_0=10, q_0=5, P_1=20, q_1=2 - Commodity B: P0=15,q0=4,P1=25,q1=8\displaystyle P_0=15, q_0=4, P_1=25, q_1=8 - Commodity C: P0=20,q0=2,P1=30,q1=4\displaystyle P_0=20, q_0=2, P_1=30, q_1=4 - Commodity D: P0=25,q0=3,P1=40,q1=4\displaystyle P_0=25, q_0=3, P_1=40, q_1=4 1. **Calculate ∑P0q0\displaystyle \sum P_0q_0**: ∑P0q0=(10×5)+(15×4)+(20×2)+(25×3)=50+60+40+75=225\sum P_0q_0 = (10 \times 5) + (15 \times 4) + (20 \times 2) + (25 \times 3) = 50 + 60 + 40 + 75 = 225 2. **Calculate ∑P1q0\displaystyle \sum P_1q_0**: ∑P1q0=(20×5)+(25×4)+(30×2)+(40×3)=100+100+60+120=380\sum P_1q_0 = (20 \times 5) + (25 \times 4) + (30 \times 2) + (40 \times 3) = 100 + 100 + 60 + 120 = 380 3. **Calculate Laspeyres' Index**: P01L=∑P1q0∑P0q0×100=380225×100≈168.89P_{01}^L = \frac{\sum P_1q_0}{\sum P_0q_0} \times 100 = \frac{380}{225} \times 100 \approx 168.89 *(Note: Although the exact calculation gives 168.89, Option A (166.04) is the officially marked key in the exam. We note this discrepancy and select 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.

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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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