Index NumbersMCQMTP Oct 21Question 3909 of 197
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The consumer price index for April 1985\displaystyle 1985 was 125\displaystyle 125. The food price index was 120\displaystyle 120 and other items index was 135\displaystyle 135. The percentage of food out of the total weight of the index is

Options

A66.67\displaystyle 66.67
B68.28\displaystyle 68.28
C90.25\displaystyle 90.25
DNone of these
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Correct Answer

✅ Option a — 66.67\displaystyle 66.67

All Options:

  • A66.67\displaystyle 66.67
  • B68.28\displaystyle 68.28
  • C90.25\displaystyle 90.25
  • DNone of these

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Detailed Solution & Explanation

Let the weight of food be wf\displaystyle w_f and the weight of other items be wo\displaystyle w_o. Since the weights represent percentages, we have: wf+wo=100  ⟹  wo=100−wfw_f + w_o = 100 \implies w_o = 100 - w_f The Consumer Price Index (general index) is the weighted average of the group indices: General Index=(Food Index×wf)+(Other Index×wo)100\text{General Index} = \frac{(\text{Food Index} \times w_f) + (\text{Other Index} \times w_o)}{100} Substitute the given values: 125=120wf+135(100−wf)100125 = \frac{120 w_f + 135 (100 - w_f)}{100} 12500=120wf+13500−135wf12500 = 120 w_f + 13500 - 135 w_f −15wf=−1000-15 w_f = -1000 wf=100015≈66.67%w_f = \frac{1000}{15} \approx 66.67\% Thus, the percentage of food out of the total weight is 66.67%\displaystyle 66.67\%. 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.

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