The ages of A and B are in the ratio `5 : 2` After 5 years their ages will be in the ratio `15 : 7` , The present age of A is

Options

A. 48 years
B. 36 years
C. 40 years
D. 35 years

Answer

To find the present age of A given the ratios of ages, we can follow these steps:

### Step 1: Set up the variables
Let the present age of A be \(5x\) and the present age of B be \(2x\), based on the ratio \(5:2\).

### Step 2: Write the expressions for their ages after 5 years
After 5 years, the age of A will be \(5x + 5\) and the age of B will be \(2x + 5\).

### Step 3: Set up the equation based on the new ratio
According to the problem, after 5 years, their ages will be in the ratio \(15:7\). This gives us the equation:
\[ \frac{5x + 5}{2x + 5} = \frac{15}{7} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 7(5x + 5) = 15(2x + 5) \]

### Step 5: Distribute both sides
Distributing on both sides results in:
\[ 35x + 35 = 30x + 75 \]

### Step 6: Rearrange the equation to isolate \(x\)
Subtract \(30x\) from both sides:
\[ 35x - 30x + 35 = 75 \]
This simplifies to:
\[ 5x + 35 = 75 \]

### Step 7: Solve for \(x\)
Subtract 35 from both sides:
\[ 5x = 75 - 35 \]
\[ 5x = 40 \]
Now, divide by 5:
\[ x = \frac{40}{5} = 8 \]

### Step 8: Find the present age of A
Now that we have \(x\), we can find the present age of A:
\[ \text{Age of A} = 5x = 5 \times 8 = 40 \]

### Conclusion
The present age of A is **40 years**.

---