A man's monthly salary is Rs.24000 and his monthly expenses on travel are Rs.2500. The central angle of the sector representing travel expenses in the pie chart would be

Options

A. `30^@`
B. `37.5^@`
C. `45^@`
D. `60^@`

Answer

To find the central angle of the sector representing travel expenses in a pie chart, we will follow these steps:

### Step 1: Understand the Total Salary and Expenses
The man's monthly salary is Rs. 24,000, and his monthly expenses on travel are Rs. 2,500.

### Step 2: Determine the Total Angle of the Circle
The total angle in a pie chart is 360 degrees.

### Step 3: Calculate the Value of 1 Degree
To find out how much each degree represents in terms of salary, we can use the formula:
\[ \text{Value of 1 degree} = \frac{\text{Total Salary}}{\text{Total Angle}} = \frac{24000}{360} \]

### Step 4: Perform the Division
Now, we will calculate:
\[ \frac{24000}{360} = \frac{24000 \div 120}{360 \div 120} = \frac{200}{3} \approx 66.67 \]
So, 1 degree of the circle represents approximately Rs. 66.67.

### Step 5: Calculate the Central Angle for Travel Expenses
Now, we need to find out how many degrees correspond to the travel expenses of Rs. 2,500. We can use the formula:
\[ \text{Central Angle (θ)} = \left(\frac{\text{Travel Expenses}}{\text{Total Salary}}\right) \times \text{Total Angle} \]
Substituting the values:
\[ \text{Central Angle (θ)} = \left(\frac{2500}{24000}\right) \times 360 \]

### Step 6: Simplify the Calculation
Calculating the fraction:
\[ \frac{2500}{24000} = \frac{25}{240} = \frac{5}{48} \]
Now, substituting this back into the angle calculation:
\[ \text{Central Angle (θ)} = \left(\frac{5}{48}\right) \times 360 \]

### Step 7: Perform the Multiplication
Calculating:
\[ \text{Central Angle (θ)} = \frac{5 \times 360}{48} = \frac{1800}{48} \]
Now simplifying:
\[ \frac{1800 \div 12}{48 \div 12} = \frac{150}{4} = 37.5 \]

### Final Answer
Thus, the central angle of the sector representing travel expenses in the pie chart is **37.5 degrees**.

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