Statistical Description of DataPYQ 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?

Options

A216\displaystyle 216
B189\displaystyle 189
C180\displaystyle 180
D99\displaystyle 99
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Correct Answer

✅ Option b — 189\displaystyle 189

All Options:

  • A216\displaystyle 216
  • B189\displaystyle 189
  • C180\displaystyle 180
  • D99\displaystyle 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\displaystyle 200 million shares). **Case 1: Standard Formulation (with FII = 25\displaystyle 25 million)** 1. Calculate the total number of shares: Total Shares=120 (Promoter)+25 (FII)+20 (DII)+20 (Govt)+15 (Public)=200 million\text{Total Shares} = 120\text{ (Promoter)} + 25\text{ (FII)} + 20\text{ (DII)} + 20\text{ (Govt)} + 15\text{ (Public)} = 200\text{ million} 2. The formula for the central angle of a category in a pie chart is: Central Angle=Shares of CategoryTotal Shares×360∘\text{Central Angle} = \frac{\text{Shares of Category}}{\text{Total Shares}} \times 360^\circ 3. Calculate the central angle for Promoters: AnglePromoter=120200×360∘=216∘\text{Angle}_{\text{Promoter}} = \frac{120}{200} \times 360^\circ = 216^\circ 4. Calculate the central angle for the Public: AnglePublic=15200×360∘=27∘\text{Angle}_{\text{Public}} = \frac{15}{200} \times 360^\circ = 27^\circ 5. Find the difference between their central angles: Difference=216∘−27∘=189∘\text{Difference} = 216^\circ - 27^\circ = 189^\circ This matches Option B. **Case 2: Literal Formulation as printed (with FII = 40\displaystyle 40 million)** 1. Calculate the total number of shares: Total Shares=120+40+20+20+15=215 million\text{Total Shares} = 120 + 40 + 20 + 20 + 15 = 215\text{ million} 2. Calculate the central angle for Promoters: AnglePromoter=120215×360∘≈200.93∘\text{Angle}_{\text{Promoter}} = \frac{120}{215} \times 360^\circ \approx 200.93^\circ 3. Calculate the central angle for the Public: AnglePublic=15215×360∘≈25.12∘\text{Angle}_{\text{Public}} = \frac{15}{215} \times 360^\circ \approx 25.12^\circ 4. Find the difference between their central angles: Difference=200.93∘−25.12∘=175.81∘\text{Difference} = 200.93^\circ - 25.12^\circ = 175.81^\circ Since 175.81∘\displaystyle 175.81^\circ is not in the options, it is clear that FII was intended to be 25\displaystyle 25 million. Correcting for the typo, the derived answer is 189∘\displaystyle 189^\circ. Hence, **Option B** is the correct answer.

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