The average age of Sita and Gita is 30 years. If Rita replaces Sita, then the average age will become 28 years and if Rita replaces Gita, then the average age will become 32 years. What are the respective ages (in years) of Sita, Gita and Rita respectively?
(a)40,44,36
(b)44, 40, 36
(c)34, 26, 30
(d)30, 26, 34

Options

A. 40, 44, 36
B. 44, 40, 36
C. 34, 26, 30
D. 30, 26, 34

Answer

To solve the problem, we will denote the ages of Sita, Gita, and Rita as S, G, and R respectively.

### Step 1: Set up the equations based on the given information.
1. The average age of Sita and Gita is 30 years:
\[ \frac{S + G}{2} = 30 \]
Multiplying both sides by 2 gives:
\[ S + G = 60 \quad \text{(Equation 1)} \]

2. If Rita replaces Sita, the average age becomes 28 years:
\[ \frac{R + G}{2} = 28 \]
Multiplying both sides by 2 gives:
\[ R + G = 56 \quad \text{(Equation 2)} \]

3. If Rita replaces Gita, the average age becomes 32 years:
\[ \frac{S + R}{2} = 32 \]
Multiplying both sides by 2 gives:
\[ S + R = 64 \quad \text{(Equation 3)} \]

### Step 2: Solve the equations.
Now we have three equations:
1. \( S + G = 60 \) (Equation 1)
2. \( R + G = 56 \) (Equation 2)
3. \( S + R = 64 \) (Equation 3)

### Step 3: Add all three equations.
Adding all three equations together:
\[ (S + G) + (R + G) + (S + R) = 60 + 56 + 64 \]
This simplifies to:
\[ 2S + 2G + 2R = 180 \]
Dividing through by 2 gives:
\[ S + G + R = 90 \quad \text{(Equation 4)} \]

### Step 4: Find Rita's age.
Now, we can find Rita's age by substituting Equation 1 into Equation 4:
\[ R = 90 - (S + G) \]
Substituting \( S + G = 60 \) from Equation 1:
\[ R = 90 - 60 = 30 \]

### Step 5: Find Gita's age.
Now substitute \( R = 30 \) into Equation 2:
\[ 30 + G = 56 \]
Solving for G gives:
\[ G = 56 - 30 = 26 \]

### Step 6: Find Sita's age.
Now substitute \( G = 26 \) into Equation 1:
\[ S + 26 = 60 \]
Solving for S gives:
\[ S = 60 - 26 = 34 \]

### Conclusion:
The ages of Sita, Gita, and Rita are:
- Sita (S) = 34 years
- Gita (G) = 26 years
- Rita (R) = 30 years

Thus, the respective ages of Sita, Gita, and Rita are **34, 26, and 30 years**.

### Final Answer:
(c) 34, 26, 30

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