Index NumbersPYQ May 25Question 4097 of 197
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From the following chain base index numbers based on 2015, find out new chain base index number for the year 2022 by shifting the base year 2019. Index No Base 2015: 2015(100), 2016(105), 2017(95), 2018(85), 2019(120), 2020(110), 2021(130), 2022(150)

Options

A125
B180
C100
D150
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Correct Answer

✅ Option a — 125

All Options:

  • A125
  • B180
  • C100
  • D150

Detailed Solution & Explanation

To shift the base year of a series of index numbers to a new base year, we use the base shifting formula:
New Index Number=Old Index Number of current yearOld Index Number of the new base year×100\text{New Index Number} = \frac{\text{Old Index Number of current year}}{\text{Old Index Number of the new base year}} \times 100 Here:
- The year to calculate is 2022. The old index for 2022 is 150\displaystyle 150.
- The new base year is 2019. The old index for 2019 is 120\displaystyle 120.

Substitute these values into the formula:
New Index Number for 2022=150120×100\text{New Index Number for 2022} = \frac{150}{120} \times 100 New Index Number for 2022=54×100=125\text{New Index Number for 2022} = \frac{5}{4} \times 100 = 125
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.

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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More Questions from Index Numbers

In price index, when a new commodity is required to be added, which of the following index is used?

Fisher's ideal formula for calculating index number satisfies the ________

Shifted Price Index = Original Price IndexPrice Index of the year on which it has to be shifted×100\displaystyle \frac{\text{Original Price Index}}{\text{Price Index of the year on which it has to be shifted}} \times 100

If Laspeyres's Index Number is 250 and Paasche's Index Number is 160, then Fisher's Index number is

If ∑P0q0=240\displaystyle \sum P_0q_0 = 240, ∑P1q0=480\displaystyle \sum P_1q_0 = 480, ∑P0q1=600\displaystyle \sum P_0q_1 = 600 and ∑P1q1=192\displaystyle \sum P_1q_1 = 192, then Laspeyres's Index Number is

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