Three years ago, the average age of Anita, Priya, and Varsha was 27 years. If five years ago, the average age of Priya and Varsha was 20 years, find the present age of Anita.

Options

A. 25
B. 60
C. 40
D. 30

Answer

To find the present age of Anita, we can follow these steps:

### Step 1: Determine the total age of Anita, Priya, and Varsha three years ago.
Given that the average age of Anita, Priya, and Varsha three years ago was 27 years, we can calculate their total age at that time.

\[ \text{Total age of A, P, and V three years ago} = \text{Average age} \times \text{Number of people} = 27 \times 3 = 81 \text{ years} \]

### Step 2: Calculate their present total age.
Since three years have passed, we need to add 3 years to each of their ages. Therefore, we add \(3 \times 3 = 9\) years to the total age calculated in Step 1.

\[ \text{Present total age of A, P, and V} = 81 + 9 = 90 \text{ years} \]

### Step 3: Determine the total age of Priya and Varsha five years ago.
We know that the average age of Priya and Varsha five years ago was 20 years. Thus, we can calculate their total age at that time.

\[ \text{Total age of P and V five years ago} = 20 \times 2 = 40 \text{ years} \]

### Step 4: Calculate their present total age.
Since five years have passed, we add \(5 \times 2 = 10\) years to the total age calculated in Step 3.

\[ \text{Present total age of P and V} = 40 + 10 = 50 \text{ years} \]

### Step 5: Set up the equation to find Anita's present age.
We know the present total age of Anita, Priya, and Varsha is 90 years, and the present total age of Priya and Varsha is 50 years. We can set up the equation:

\[ A + P + V = 90 \]
\[ P + V = 50 \]

### Step 6: Substitute to find Anita's age.
We can substitute the second equation into the first equation to find Anita's age:

\[ A + (P + V) = 90 \]
\[ A + 50 = 90 \]

Now, solving for \(A\):

\[ A = 90 - 50 = 40 \text{ years} \]

### Conclusion
The present age of Anita is 40 years.

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