Statistical Representation of DataMCQPYQ Jun 23Question 2643 of 295
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The share holding pattern of ABC Ltd. is as follows:Share holdersNo. of shares in MillionsPromoter120FII40DII20Govt20Public15What is the difference between central angles (in degree) for shares held by Promoters and Public, in pie chart?

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

✅ Option b — $189$

All Options:

  • A$216$
  • B$189$
  • C$180$
  • D$99$

Detailed Solution & Explanation

Let us analyze the shareholding pattern to find the central angles. The question text contains a typographical error stating "FII 40" instead of "FII 25" (which is standard for this past exam question to give a total of $200$ million shares). **Case 1: Standard Formulation (with FII = $25$ million)** 1. Calculate the total number of shares: Total Shares=120 (Promoter)+25 (FII)+20 (DII)+20 (Govt)+15 (Public)=200 millionTotal Shares=120\displaystyle \text{Total Shares} = 120 (Promoter)+25\displaystyle \text{ (Promoter)} + 25 (FII)+20\displaystyle \text{ (FII)} + 20 (DII)+20\displaystyle \text{ (DII)} + 20 (Govt)+15\displaystyle \text{ (Govt)} + 15 (Public)=200\displaystyle \text{ (Public)} = 200 million\displaystyle \text{ million} 2. The formula for the central angle of a category in a pie chart is: Central Angle=Shares of CategoryTotal Shares×360∘\displaystyle \text{Central Angle} = \frac{Shares of Category\displaystyle \text{Shares of Category}}{Total Shares\displaystyle \text{Total Shares}} ×\displaystyle \times 360^\circ 3. Calculate the central angle for Promoters: AnglePromoter=120200×360∘=216∘Angle\displaystyle \text{Angle}_{Promoter\displaystyle \text{Promoter}} = 120200\displaystyle \frac{120}{200} ×\displaystyle \times 360^\circ = 216^\circ 4. Calculate the central angle for the Public: AnglePublic=15200×360∘=27∘Angle\displaystyle \text{Angle}_{Public\displaystyle \text{Public}} = 15200\displaystyle \frac{15}{200} ×\displaystyle \times 360^\circ = 27^\circ 5. Find the difference between their central angles: Difference=216∘−27∘=189∘\displaystyle \text{Difference} = 216^\circ - 27^\circ = 189^\circ This matches Option B. **Case 2: Literal Formulation as printed (with FII = $40$ million)** 1. Calculate the total number of shares: Total Shares=120+40+20+20+15=215 millionTotal Shares=120+40+20+20+15=215\displaystyle \text{Total Shares} = 120 + 40 + 20 + 20 + 15 = 215 million\displaystyle \text{ million} 2. Calculate the central angle for Promoters: AnglePromoter=120215×360∘≈200.93∘Angle\displaystyle \text{Angle}_{Promoter\displaystyle \text{Promoter}} = 120215\displaystyle \frac{120}{215} ×\displaystyle \times 360^\circ ≈\displaystyle \approx 200.93^\circ 3. Calculate the central angle for the Public: AnglePublic=15215×360∘≈25.12∘Angle\displaystyle \text{Angle}_{Public\displaystyle \text{Public}} = 15215\displaystyle \frac{15}{215} ×\displaystyle \times 360^\circ ≈\displaystyle \approx 25.12^\circ 4. Find the difference between their central angles: Difference=200.93∘−25.12∘=175.81∘Difference=200\displaystyle \text{Difference} = 200.93^\circ - 25.12^\circ = 175.81^\circ Since $175.81^\circ$ is not in the options, it is clear that FII was intended to be $25$ million. Correcting for the typo, the derived answer is $189^\circ$. Hence, **Option B** is the correct answer.

About This Chapter: Statistical Representation of Data

Paper

Paper 3: Quantitative Aptitude

Weightage

2-4 Marks

Key Topics

Data, Frequency Distribution, Graphical Representation

This chapter covers Data, Frequency Distribution, Graphical Representation and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 2-4 Marks weightage. Focus on understanding core concepts rather than memorizing.

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