The present ages of Vikas and Vishal are in the ratio 15: 8. After ten years, their ages will be in the ratio 5:3. Find their present ages.

Options

A. 60 years, 32 years
B. 32 years, 60 years
C. 15 years, 8 years
D. 8 years, 15 years

Answer

To find the present ages of Vikas and Vishal, we can follow these steps:

### Step 1: Define the present ages
Let the present age of Vikas be \( 15x \) and the present age of Vishal be \( 8x \), where \( x \) is a common multiplier.

### Step 2: Set up the equation for their ages after 10 years
After 10 years, Vikas's age will be \( 15x + 10 \) and Vishal's age will be \( 8x + 10 \).

### Step 3: Write the ratio of their ages after 10 years
According to the problem, after 10 years, their ages will be in the ratio of \( 5:3 \). Therefore, we can write the equation:
\[ \frac{15x + 10}{8x + 10} = \frac{5}{3} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 3(15x + 10) = 5(8x + 10) \]

### Step 5: Expand both sides
Expanding both sides results in:
\[ 45x + 30 = 40x + 50 \]

### Step 6: Rearrange the equation
Now, we will rearrange the equation to isolate \( x \):
\[ 45x - 40x = 50 - 30 \]
\[ 5x = 20 \]

### Step 7: Solve for \( x \)
Dividing both sides by 5 gives:
\[ x = 4 \]

### Step 8: Find the present ages
Now we can find the present ages of Vikas and Vishal:
- Vikas's age: \( 15x = 15 \times 4 = 60 \)
- Vishal's age: \( 8x = 8 \times 4 = 32 \)

### Conclusion
Thus, the present ages of Vikas and Vishal are:
- Vikas: 60 years
- Vishal: 32 years

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