Expenses (in multiples of ₹10,000/-) on consumption of fuel for the official car at a regional office (RO) of a national organization during 2006-2010 is given below in a tabular form along with the National Average (NA) during the said period. It is given that there are five ROs.
`{:("Year",2006,2007,2008,2009,2010),("RO",20,22,23,24,25),("NA",18,17,19,18,23):}`
If the data of the RO is represented through a pie chart, Then what would be the central angle (nearest to degree) of the sector corresponding to the year 2008?
(a)`68^(@)`
(b)`70^(@)`
(c)`76^(@)`
(d)`73^(@)`

Options

A. `68^(@)`
B. `70^(@)`
C. `76^(@)`
D. `73^(@)`

Answer

To find the central angle of the sector corresponding to the year 2008 in a pie chart representing the expenses of the regional office (RO), we will follow these steps:

### Step 1: Sum the expenses for the RO from 2006 to 2010
The expenses for the RO from the table are:
- 2006: 20
- 2007: 22
- 2008: 23
- 2009: 24
- 2010: 25

Now, we will sum these values:
\[ \text{Total Expenses} = 20 + 22 + 23 + 24 + 25 = 114 \]

### Step 2: Determine the total angle of the pie chart
The total angle of a pie chart is always 360 degrees.

### Step 3: Calculate the value of one unit in degrees
To find the angle corresponding to one unit of expense, we divide the total angle by the total expenses:
\[ \text{Angle per unit} = \frac{360 \text{ degrees}}{114} \approx 3.1579 \text{ degrees} \]

### Step 4: Find the angle for the year 2008
The expense for the year 2008 is 23. To find the central angle for this year, we multiply the expense by the angle per unit:
\[ \text{Central Angle for 2008} = 23 \times 3.1579 \approx 72.45 \text{ degrees} \]

### Step 5: Round to the nearest degree
Rounding 72.45 degrees to the nearest whole number gives us:
\[ \text{Central Angle for 2008} \approx 73 \text{ degrees} \]

### Conclusion
The central angle corresponding to the year 2008 is approximately **73 degrees**.

### Final Answer
(d) 73^(@)

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