The ratio of ages of A & B before 5 years was 2:3. If the sum of ages of A&B at present is 45 years. Find the present ages of A&B.

Answer

To solve the problem step by step, we will follow the information provided in the question.

### Step 1: Understand the given information
The ratio of ages of A and B before 5 years was 2:3. This means that if we denote A's age 5 years ago as \(2x\) and B's age 5 years ago as \(3x\), we can express their ages in terms of a variable \(x\).

### Step 2: Set up the equation for their ages 5 years ago
Let:
- A's age 5 years ago = \(2x\)
- B's age 5 years ago = \(3x\)

### Step 3: Calculate the total age 5 years ago
The total age of A and B 5 years ago would be:
\[ 2x + 3x = 5x \]

### Step 4: Relate the total age 5 years ago to the present age
Since the present age of A and B combined is 45 years, we can find their total age 5 years ago:
\[ \text{Total age 5 years ago} = \text{Present age} - 10 = 45 - 10 = 35 \]
Thus, we have:
\[ 5x = 35 \]

### Step 5: Solve for \(x\)
Now, we can solve for \(x\):
\[ x = \frac{35}{5} = 7 \]

### Step 6: Find the ages of A and B 5 years ago
Now that we have \(x\), we can find the ages of A and B 5 years ago:
- A's age 5 years ago = \(2x = 2 \times 7 = 14\)
- B's age 5 years ago = \(3x = 3 \times 7 = 21\)

### Step 7: Find the present ages of A and B
To find their present ages, we add 5 years to their ages 5 years ago:
- Present age of A = \(14 + 5 = 19\)
- Present age of B = \(21 + 5 = 26\)

### Final Answer
- Present age of A = 19 years
- Present age of B = 26 years

---