The prices and quantities of 3 commodities in base and current years are as follows: P0 | P1 | Q0 | Q1 12 | 14 | 10 | 2010 | 8 | 20 | 308 | 10 | 30 | 10The Laspeyre's Price Index Number is:

Option b: 107.14. Solution: Let's compute the sums of products of prices and quantities from the given table: - Commodity 1: P0 = 12, P1 = 14, Q0 = 10, Q1 = 20 - Commodity 2: P0 = 10, P1 = 8, Q0 = 20, Q1 = 30 - Commodity 3: P0 = 8, P1 = 10, Q0 = 30, Q1 = 10 1. Calculate sum P0Q0 : sum P0Q0 = (12 × 10) + (10 × 20) + (8 × 30) = 120 + 200 + 240 = 560 2. Calculate sum P1Q0 : sum P1Q0 = (14 × 10) + (8 × 20) + (10 × 30) = 140 + 160 + 300 = 600 3. Calculate Laspeyres Price Index: P01L = sum P1Q0/sum P0Q0 × 100 = 600/560 × 100 ≈ 107.14 This matches Option B. Hence, Option B is the correct answer.

Index NumbersMCQMTP Dec 22 Series IIQuestion 3918 of 197

All Questions

The prices and quantities of $\displaystyle 3$ commodities in base and current years are as follows: $\displaystyle P_0$ | $\displaystyle P_1$ | $\displaystyle Q_0$ | $\displaystyle Q_1$ 12 | 14 | 10 | 2010 | 8 | 20 | 308 | 10 | 30 | 10The Laspeyre's Price Index Number is:

Options

\displaystyle 118.13

\displaystyle 107.14

\displaystyle 120.10

DNone of these

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

Correct Answer

✅ Option b — $\displaystyle 107.14$

All Options:

A $\displaystyle 118.13$
B $\displaystyle 107.14$
C $\displaystyle 120.10$
DNone of these

Detailed Solution & Explanation

Let's compute the sums of products of prices and quantities from the given table: - Commodity 1:

\displaystyle P_0 = 12, P_1 = 14, Q_0 = 10, Q_1 = 20

- Commodity 2:

\displaystyle P_0 = 10, P_1 = 8, Q_0 = 20, Q_1 = 30

- Commodity 3:

\displaystyle P_0 = 8, P_1 = 10, Q_0 = 30, Q_1 = 10

1. **Calculate

\displaystyle \sum P_0Q_0

**:

\sum P_0Q_0 = (12 \times 10) + (10 \times 20) + (8 \times 30) = 120 + 200 + 240 = 560

2. **Calculate

\displaystyle \sum P_1Q_0

**:

\sum P_1Q_0 = (14 \times 10) + (8 \times 20) + (10 \times 30) = 140 + 160 + 300 = 600

3. **Calculate Laspeyres Price Index**:

P_{01}^L = \frac{\sum P_1Q_0}{\sum P_0Q_0} \times 100 = \frac{600}{560} \times 100 \approx 107.14

This matches 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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The prices and quantities of 3\displaystyle 33 commodities in base and current years are as follows:P0\displaystyle P_0P0​ | P1\displaystyle P_1P1​ | Q0\displaystyle Q_0Q0​ | Q1\displaystyle Q_1Q1​12 | 14 | 10 | 2010 | 8 | 20 | 308 | 10 | 30 | 10The Laspeyre's Price Index Number is: