Index NumbersPYQ Sept 25Question 4495 of 197
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Two indices that is current on base and base on current should be reciprocals of each other in

Options

AUnit test
BTime reversal test
CCircular test
DAverage weighted test
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Correct Answer

✅ Option b — Time reversal test

All Options:

  • AUnit test
  • BTime reversal test
  • CCircular test
  • DAverage weighted test

Detailed Solution & Explanation

Let us review the adequacy tests for index numbers from first principles:
1. **Time Reversal Test**: This test requires that if the base period and the current period are interchanged, the resulting index numbers should be reciprocals of each other. Mathematically, if P01\displaystyle P_{01} represents the index of the current period 1\displaystyle 1 with base period 0\displaystyle 0, and P10\displaystyle P_{10} represents the index of period 0\displaystyle 0 with base period 1\displaystyle 1, then:
P01×P10=1  ⟹  P10=1P01P_{01} \times P_{10} = 1 \implies P_{10} = \frac{1}{P_{01}}
2. **Other tests**:
- **Unit Test**: Requires that the index number formula should be independent of the physical units of measurement.
- **Circular Test**: An extension of the time reversal test for more than two periods, requiring P01×P12×P20=1\displaystyle P_{01} \times P_{12} \times P_{20} = 1.
- **Factor Reversal Test**: Requires that the product of the price index and quantity index equals the value ratio.
Therefore, the test requiring current-on-base and base-on-current indices to be reciprocals is the Time Reversal Test.
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.

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