The ratio between the present ages of A and B is 3:5 respectively. If the difference between B's present age and A's age after 4 years is 2 , what is the total of A's and B's present ages?

Options

A. a. 24 years
B. b. 32 year
C. c. 48 years
D. d. None of these

Answer

To solve the problem step by step, we will use the information given about the ages of A and B.

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

### Step 2: Set up the equation based on the given condition
According to the problem, the difference between B's present age and A's age after 4 years is 2. We can express this mathematically as:
\[ B - (A + 4) = 2 \]
Substituting the expressions for A and B, we have:
\[ 5x - (3x + 4) = 2 \]

### Step 3: Simplify the equation
Now, simplify the equation:
\[ 5x - 3x - 4 = 2 \]
This simplifies to:
\[ 2x - 4 = 2 \]

### Step 4: Solve for \(x\)
Next, we will solve for \(x\):
\[ 2x = 2 + 4 \]
\[ 2x = 6 \]
\[ x = 3 \]

### Step 5: Calculate the present ages of A and B
Now that we have the value of \(x\), we can find the present ages of A and B:
- A's present age:
\[ A = 3x = 3 \times 3 = 9 \]
- B's present age:
\[ B = 5x = 5 \times 3 = 15 \]

### Step 6: Calculate the total of A's and B's present ages
Finally, we can find the total of A's and B's present ages:
\[ \text{Total} = A + B = 9 + 15 = 24 \]

### Conclusion
The total of A's and B's present ages is **24 years**.

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