If Sigma p0q0 = 160.7 and Sigma p1q0 = 178.6 , then the cost of living index is

Option a: 111.14. Solution: Let us calculate the Cost of Living Index (also known as the consumer price index) using the weighted aggregative method (Laspeyres' formula): 1. Formula for Cost of Living Index: Cost of Living Index = sum p1 q0/sum p0 q0 × 100 where p1 and p0 represent the current and base year prices, and q0 represents the base year quantities (weights). 2. Given Data: - sum p0 q0 = 160.7 - sum p1 q0 = 178.6 3. Calculation: Substitute the given values into the formula: Cost of Living Index = 178.6/160.7 × 100 Cost of Living Index ≈ 1.111387 × 100 ≈ 111.14 Therefore, the cost of living index is 111.14 . Hence, Option A is the correct answer.

If $\Sigma p_0q_0 = 160.7$ and $\Sigma p_1q_0 = 178.6$, then the cost of living index is

The correct answer is Option a: 111.14. Let us calculate the Cost of Living Index (also known as the consumer price index) using the weighted aggregative method (Laspeyres' formula): 1. **Formula for Cost of Living Index**: $$\text{Cost of Living Index} = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100$$ where $p_1$ and $p_0$ represent the current and base year prices, and $q_0$ represents the base year quantities (weights). 2. **Given Data**: - $\sum p_0 q_0 = 160.7$ - $\sum p_1 q_0 = 178.6$ 3. **Calculation**: Substitute the given values into the formula: $$\text{Cost of Living Index} = \frac{178.6}{160.7} \times 100$$ $$\text{Cost of Living Index} \approx 1.111387 \times 100 \approx 111.14$$ Therefore, the cost of living index is $111.14$. Hence, **Option A** is the correct answer.

Index NumbersPYQ Sept 25Question 4196 of 197

All Questions

If $\displaystyle \Sigma p_0q_0 = 160.7$ and $\displaystyle \Sigma p_1q_0 = 178.6$ , then the cost of living index is

Options

A111.14

B93.10

C104.71

D105.7

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

Correct Answer

✅ Option a — 111.14

All Options:

A111.14
B93.10
C104.71
D105.7

Detailed Solution & Explanation

Let us calculate the Cost of Living Index (also known as the consumer price index) using the weighted aggregative method (Laspeyres' formula):
1. **Formula for Cost of Living Index**:

\text{Cost of Living Index} = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100

where

\displaystyle p_1

and

\displaystyle p_0

represent the current and base year prices, and

\displaystyle q_0

represents the base year quantities (weights).
2. **Given Data**:
-

\displaystyle \sum p_0 q_0 = 160.7

\displaystyle \sum p_1 q_0 = 178.6

3. **Calculation**:
Substitute the given values into the formula:

\text{Cost of Living Index} = \frac{178.6}{160.7} \times 100

\text{Cost of Living Index} \approx 1.111387 \times 100 \approx 111.14

Therefore, the cost of living index is

\displaystyle 111.14

.
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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If Σp0q0=160.7\displaystyle \Sigma p_0q_0 = 160.7Σp0​q0​=160.7 and Σp1q0=178.6\displaystyle \Sigma p_1q_0 = 178.6Σp1​q0​=178.6, then the cost of living index is