Index NumbersMCQPYQ June 19Question 3878 of 197
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The cost of living index numbers in years 2015 and 2018 were 97.5 and 115 respectively. The salary of a worker in 2015 was $19500$. How much additional salary was required for him in 2018 to maintain the same standard of living as in 2015?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — $3500$

All Options:

  • A$3000$
  • B$4000$
  • C$3500$
  • D$4500$

Detailed Solution & Explanation

We are given: - Cost of living index (CLI) in base year (2015) = $97.5$ - Cost of living index (CLI) in current year (2018/2021) = $115$ - Salary in base year (2015) = 19,500 To maintain the same standard of living, the salary in the current year should be adjusted proportionally to the CLI: Required Salary=Base Salary×Current CLIBase CLI=19,500×11597.5=23,000.00\displaystyle \text{Required Salary} = \text{Base Salary} ×\displaystyle \times Current CLIBase CLI=19\displaystyle \frac{\text{Current CLI}}{\text{Base CLI}} = 19,500 ×\displaystyle \times 11597.5=23\displaystyle \frac{115}{97.5} = 23,000.00 Therefore, the additional salary required is: Additional Salary=Required Salary−Base Salary=23,000.00−19,500=3,500.00\displaystyle \text{Additional Salary} = \text{Required Salary} - Base Salary=23\displaystyle \text{Base Salary} = 23,000.00 - 19,500 = 3,500.00 This matches 3,500. Hence, **Option C** 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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If ∑P0q0=240\displaystyle ∑\displaystyle \sum P_0q_0 = 240, ∑P1q0=480\displaystyle ∑\displaystyle \sum P_1q_0 = 480, ∑P0q1=600\displaystyle ∑\displaystyle \sum P_0q_1 = 600 and ∑P1q1=192\displaystyle ∑\displaystyle \sum P_1q_1 = 192, then Laspeyres's Index Number is

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