Index NumbersMCQPYQ Dec 23Question 3890 of 197
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The gross monthly pay of an employee was $15,000$ in a year $2020$. The consumer price index number in $2023\displaystyle is $155 with $2020$ as base year. If employee is to rightly compensate what dearness allowance is required to be paid?

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

✅ Option b — $8,250$

All Options:

  • A$8,000$
  • B$8,250$
  • C$8,500$
  • D$8,750$

Detailed Solution & Explanation

We are given: - Base year pay (2020) = $15,000$ - CPI in current year (2023) = $155$ (with base year as 100) The required pay in 2023 to maintain the same standard of living is: Required Pay=Base Pay×CPI100=15000×155100=23250\displaystyle \text{Required Pay} = \text{Base Pay} ×\displaystyle \times CPI100=15000\displaystyle \frac{\text{CPI}}{100} = 15000 ×\displaystyle \times 155100=23250\displaystyle \frac{155}{100} = 23250 The Dearness Allowance (DA) is the additional compensation required to bridge this gap: DA Required=Required Pay−Base Pay=23250−15000=8250\displaystyle \text{DA Required} = \text{Required Pay} - Base Pay=23250−15000=8250\displaystyle \text{Base Pay} = 23250 - 15000 = 8250 Alternatively: DA=Base Pay×CPI−100100=15000×0.55=8250\displaystyle \text{DA} = \text{Base Pay} ×\displaystyle \times CPI−100100=15000\displaystyle \frac{\text{CPI} - 100}{100} = 15000 ×\displaystyle \times 0.55 = 8250 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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If Laspeyres's Index Number is 250 and Paasche's Index Number is 160, then Fisher's Index number is

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

If ΣPnqn=249\displaystyle Σ\displaystyle \Sigma P_n q_n = 249, ΣP0q0=150\displaystyle Σ\displaystyle \Sigma P_0 q_0 = 150, ΣPnq0=145\displaystyle Σ\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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