Index NumbersMCQMTP Dec 23 Series IIQuestion 3927 of 197
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In $2017\displaystyle the average price of a commodity was $20\% more than in $2016\displaystyle but $20\% less than in $2015\displaystyle ; and more over it was $50\% more than in $2018$ to price relatives using $2016$ as base ($2016$ price relative $100$) deduce the data is:

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

✅ Option b — $150, 100, 120, 80$ (2015-18)

All Options:

  • A$120, 100, 120, 80$ (2015-18)
  • B$150, 100, 120, 80$ (2015-18)
  • C$135, 100, 125, 87$ (2015-18)
  • DNone of these

Detailed Solution & Explanation

Let the price in 2016 be P16\displaystyle P_{16} (price relative = $100\%$). - We are given that the average price in 2017 was $20\%$ more than in 2016: P17=1.20P16  ⟹  Price Relative of 2017=120P_{17} = 1.20 P_{16} \implies Price Relative of 2017=120\displaystyle \text{Price Relative of 2017} = 120 - The price in 2017 was $20\%$ less than in 2015: P17=0.80P15  ⟹  P15=P170.80=1.20P160.80=1.50P16  ⟹  Price Relative of 2015=150P_{17} = 0.80 P_{15} \implies P_{15} = \displaystyle \frac{P_{17}}{0.80} = \frac{1.20 P_{16}}{0.80} = 1.50 P_{16} \implies Price Relative of 2015=150\displaystyle \text{Price Relative of 2015} = 150 - The price in 2017 was $50\%$ more than in 2018: P17=1.50P18  ⟹  P18=P171.50=1.20P161.50=0.80P16  ⟹  Price Relative of 2018=80P_{17} = 1.50 P_{18} \implies P_{18} = \displaystyle \frac{P_{17}}{1.50} = \frac{1.20 P_{16}}{1.50} = 0.80 P_{16} \implies Price Relative of 2018=80\displaystyle \text{Price Relative of 2018} = 80 Therefore, the price relatives for 2015, 2016, 2017, 2018 in order are: 150,100,120,80150, 100, 120, 80 This matches Option B. 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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