4 years ago , the ratio of Vikah's to Rahul's age was `3 : 5` . After 6 years this ratio would become `4 :5` . Find the present age of Rahul .

Options

A. 10
B. 15
C. 14
D. 17

Answer

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

### Step 1: Define the Variables
Let the ages of Vika and Rahul 4 years ago be represented as:
- Vika's age = 3x
- Rahul's age = 5x

### Step 2: Express Present Ages
Since these ages are from 4 years ago, we can express their present ages as:
- Vika's present age = 3x + 4
- Rahul's present age = 5x + 4

### Step 3: Set Up the Future Ratio
After 6 years, their ages will be:
- Vika's age = (3x + 4) + 6 = 3x + 10
- Rahul's age = (5x + 4) + 6 = 5x + 10

According to the problem, the ratio of their ages after 6 years will be 4:5. Therefore, we can set up the equation:
\[ \frac{3x + 10}{5x + 10} = \frac{4}{5} \]

### Step 4: Cross-Multiply
Cross-multiplying gives us:
\[ 5(3x + 10) = 4(5x + 10) \]
Expanding both sides:
\[ 15x + 50 = 20x + 40 \]

### Step 5: Solve for x
Rearranging the equation:
\[ 15x + 50 - 40 = 20x \]
\[ 10 = 20x - 15x \]
\[ 10 = 5x \]
Dividing both sides by 5:
\[ x = 2 \]

### Step 6: Find Present Age of Rahul
Now, substituting x back into the expression for Rahul's present age:
\[ \text{Rahul's present age} = 5x + 4 = 5(2) + 4 = 10 + 4 = 14 \]

Thus, the present age of Rahul is **14 years**.

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