The ratio between present ages of Ritu and Priya is `3:5`. After 6 years, this ratio becomes `2:3`. Find the present age of Priya ?

Options

A. 25 years
B. 32 years
C. 30 years
D. 27 years

Explanation

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

### Step 1: Set up the ratio of their present ages
Given that the ratio of the present ages of Ritu and Priya is 3:5, we can express their ages in terms of a variable \(X\):
- Ritu's present age = \(3X\)
- Priya's present age = \(5X\)

### Step 2: Set up the equation for their ages after 6 years
After 6 years, the ages of Ritu and Priya will be:
- Ritu's age after 6 years = \(3X + 6\)
- Priya's age after 6 years = \(5X + 6\)

According to the problem, the ratio of their ages after 6 years becomes 2:3. Therefore, we can set up the following equation:
\[ \frac{3X + 6}{5X + 6} = \frac{2}{3} \]

### Step 3: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 3(3X + 6) = 2(5X + 6) \]

### Step 4: Expand both sides of the equation
Expanding both sides results in:
\[ 9X + 18 = 10X + 12 \]

### Step 5: Rearrange the equation to solve for \(X\)
Now, we can rearrange the equation to isolate \(X\):
\[ 9X + 18 - 12 = 10X \]
\[ 6 = 10X - 9X \]
\[ 6 = X \]

### Step 6: Calculate Priya's present age
Now that we have the value of \(X\), we can find Priya's present age:
\[ \text{Priya's present age} = 5X = 5 \times 6 = 30 \]

### Conclusion
Thus, the present age of Priya is **30 years**.

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