Index NumbersMCQPYQ Sep 24Question 3895 of 197
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During a certain period the cost of living index goes up from 110\displaystyle 110 to 200\displaystyle 200 and the salary of a worker is also raised from 330\displaystyle 330 to 500\displaystyle 500. Then in the real terms, the raise in salary is effectively-

Options

AGain by 75\displaystyle 75
BGain by 50\displaystyle 50
CLoss by 90\displaystyle 90
DLoss by 50\displaystyle 50
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Correct Answer

Option dLoss by 50\displaystyle 50

All Options:

  • AGain by 75\displaystyle 75
  • BGain by 50\displaystyle 50
  • CLoss by 90\displaystyle 90
  • DLoss by 50\displaystyle 50

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Detailed Solution & Explanation

We are given: - Initial Cost of Living Index (CLI0\displaystyle CLI_0) = 110\displaystyle 110 - Final Cost of Living Index (CLI1\displaystyle CLI_1) = 200\displaystyle 200 - Initial Salary (S0\displaystyle S_0) = 330\displaystyle 330 - Final Salary (S1\displaystyle S_1) = 500\displaystyle 500 Let's calculate the real wages for both periods: 1. **Real Wage in Initial Period**: RW0=S0CLI0×100=330110×100=300RW_0 = \frac{S_0}{CLI_0} \times 100 = \frac{330}{110} \times 100 = 300 2. **Real Wage in Final Period**: RW1=S1CLI1×100=500200×100=250RW_1 = \frac{S_1}{CLI_1} \times 100 = \frac{500}{200} \times 100 = 250 3. **Change in Real Terms**: ΔRW=RW1RW0=250300=50\Delta RW = RW_1 - RW_0 = 250 - 300 = -50 Since the real wage has decreased by 50\displaystyle 50, the worker has suffered a **Loss by 50**. 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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