The ratio in the ages of A and B, 1 year ago was 3 : 4. While it will be 5 : 6 after 1 year. What is the present age of B ?

Options

A. 8 years
B. 4 years
C. 6 years
D. None of these

Answer

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

### Step 1: Define Variables
Let the age of A one year ago be \(3X\) and the age of B one year ago be \(4X\).

### Step 2: Express Present Ages
The present age of A would be:
\[ \text{Present age of A} = 3X + 1 \]
The present age of B would be:
\[ \text{Present age of B} = 4X + 1 \]

### Step 3: Set Up the Ratio After One Year
After one year, the ages will be:
- Age of A: \(3X + 2\)
- Age of B: \(4X + 2\)

According to the problem, the ratio of their ages after one year is \(5:6\). Therefore, we can write the equation:
\[ \frac{3X + 2}{4X + 2} = \frac{5}{6} \]

### Step 4: Cross Multiply to Solve for X
Cross-multiplying gives us:
\[ 6(3X + 2) = 5(4X + 2) \]
Expanding both sides:
\[ 18X + 12 = 20X + 10 \]

### Step 5: Rearrange the Equation
Rearranging the equation to isolate \(X\):
\[ 18X + 12 - 10 = 20X \]
\[ 18X + 2 = 20X \]
\[ 2 = 20X - 18X \]
\[ 2 = 2X \]
\[ X = 1 \]

### Step 6: Calculate Present Age of B
Now that we have \(X\), we can find the present age of B:
\[ \text{Present age of B} = 4X + 1 = 4(1) + 1 = 4 + 1 = 5 \]

### Conclusion
The present age of B is **5 years**.

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