The ratio between the present ages of A and B is 3:5. If the ratio of their ages five years hence becomes 13:20, then the present age of B is:
A और B की वर्तमान आयु के बीच का अनुपात 3: 5 है। पाँच वर्ष बाद उनकी आयु का अनुपात 13:20 हो जाता है, तो B की वर्तमान आयु है

Options

A. 32 Years
B. 35 Years
C. 30 Years
D. 40 Years

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the present ages of A and B
Let the present age of A be \(3x\) and the present age of B be \(5x\), based on the given ratio of their ages which is 3:5.

### Step 2: Calculate their ages five years hence
In five years, the age of A will be \(3x + 5\) and the age of B will be \(5x + 5\).

### Step 3: Set up the equation based on the new ratio
According to the problem, the ratio of their ages five years hence is 13:20. Therefore, we can set up the following equation:
\[ \frac{3x + 5}{5x + 5} = \frac{13}{20} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 20(3x + 5) = 13(5x + 5) \]

### Step 5: Expand both sides of the equation
Expanding both sides results in:
\[ 60x + 100 = 65x + 65 \]

### Step 6: Rearrange the equation to isolate x
Now, we will rearrange the equation to isolate \(x\):
\[ 60x + 100 - 65x - 65 = 0 \]
\[ -5x + 35 = 0 \]
\[ 5x = 35 \]
\[ x = 7 \]

### Step 7: Calculate the present age of B
Now, we can find the present age of B:
\[ \text{Present age of B} = 5x = 5 \times 7 = 35 \]

### Conclusion
Thus, the present age of B is **35 years**.

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