The data below record and itemwise quarterly expenditure of a private organization:
`|{:("Item of expenditure","Amount (in lakh rupees)"),("1. Salaries",6.0),("2. TA & DA",4.9),("3. House rent and postage",3.6),("4. All other expenses",5.5),("Total : ",ulbar(20.0)):}|`
The data is represented by a pie diagram. what is the sectrorial angle of the sector with largest area?

Options

A. `120^(@)`
B. `108^(@)`
C. `100^(@)`
D. `90^(@)`

Explanation

To find the sectorial angle of the sector with the largest area in a pie chart representing the quarterly expenditure of a private organization, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Largest Expenditure**:
- From the given data, the expenditures are:
- Salaries: 6.0 lakh
- TA & DA: 4.9 lakh
- House rent and postage: 3.6 lakh
- All other expenses: 5.5 lakh
- The largest expenditure is **Salaries (6.0 lakh)**.

2. **Calculate the Total Expenditure**:
- The total expenditure is given as **20.0 lakh**.

3. **Calculate the Sectorial Angle**:
- The formula to calculate the sectorial angle (θ) in a pie chart is:
\[ \theta = \left(\frac{\text{Amount of the sector}}{\text{Total amount}}\right) \times 360^\circ \]
- Substituting the values:
\[ \theta = \left(\frac{6.0}{20.0}\right) \times 360^\circ \]

4. **Perform the Calculation**:
- First, simplify the fraction:
\[ \frac{6.0}{20.0} = 0.3 \]
- Now, multiply by 360:
\[ \theta = 0.3 \times 360^\circ = 108^\circ \]

5. **Conclusion**:
- The sectorial angle of the sector with the largest area (Salaries) is **108 degrees**.