Anand's income and expenditure are in the ratio 5: 2. Find the central angle of the sector, which represents Anand's savings.

Options

A. `144 ^(@)`
B. `108^(@)`
C. `90^(@)`
D. `216^(@)`

Answer

To find the central angle of the sector that represents Anand's savings, we can follow these steps:

### Step 1: Understand the Ratios
Anand's income and expenditure are given in the ratio of 5:2. This means for every 5 parts of income, there are 2 parts of expenditure.

### Step 2: Assign Variables
Let’s denote Anand's income as \( 5x \) and his expenditure as \( 2x \), where \( x \) is a common multiplier.

### Step 3: Calculate Savings
To find Anand's savings, we subtract his expenditure from his income:
\[ \text{Savings} = \text{Income} - \text{Expenditure} = 5x - 2x = 3x \]

### Step 4: Total Parts in the Ratio
Now, we need to find the total parts represented in the ratio of income and expenditure:
\[ \text{Total Parts} = \text{Income parts} + \text{Expenditure parts} + \text{Savings parts} = 5 + 2 + 3 = 10 \]

### Step 5: Calculate the Central Angle for Total Income
The total angle in a pie chart is \( 360^\circ \). Since the total parts are 10, we can find the angle represented by each part:
\[ \text{Angle per part} = \frac{360^\circ}{10} = 36^\circ \]

### Step 6: Calculate the Central Angle for Savings
Now, we can find the central angle that represents Anand's savings, which is 3 parts:
\[ \text{Central Angle for Savings} = \text{Savings parts} \times \text{Angle per part} = 3 \times 36^\circ = 108^\circ \]

### Final Answer
The central angle of the sector that represents Anand's savings is \( 108^\circ \).

---