The ratio of present ages of A to B is 3:4, X years ago the ratio was 5: 7 and sum of ages of A and B after X years is 48. Find the present age of B.

To find the present age of B, we can break down the problem into logical algebraic steps.
Let the present age of A be $3k$ and the present age of B be $4k$, where $k$ is a common constant multiplier based on the given ratio of 3:4.

Step 1: Express the ages after X years and use the sum of ages
After $X$ years:
The age of A will be $3k+X$
The age of B will be $4k+X$

According to the problem, the sum of their ages after $X$ years is 48:
$(3k+X)+(4k+X)=48$
Simplifying the equation:
$7k+2X=48$ —— (Equation 1)

Step 2: Express the ages X years ago and use the ratio
$X$ years ago:
The age of A was $3k-X$
The age of B was $4k-X$

The ratio of their ages $X$ years ago was 5:7:
$\frac{3k-X}{4k-X}=\frac{5}{7}$
Cross-multiplying to solve for $X$ in terms of $k$:
$7(3k-X)=5(4k-X)$
$21k-7X=20k-5X$
Subtracting $20k$ from both sides and adding $7X$ to both sides:
$k=2X$ —— (Equation 2)

Step 3: Solve the equations to find the value of k
Substitute the value of $2X$ from Equation 2 into Equation 1:
$7k+k=48$
$8k=48$
$k=6$

Step 4: Calculate the present age of B
The present age of B is $4k$:
$\text{Present age of B}=4\times 6=24\text{years}$

Thus, the present age of B is 24 years.