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.

The correct answer is 24 years.

Let's define the present ages of A and B based on the given ratio of 3:4. Let the present age of A be $3k$ and the present age of B be $4k$, where $k$ is a common constant multiplier.

According to the problem, $X$ years ago, the ratio of their ages was 5:7. We can write this relation as:
$\frac{3k-X}{4k-X}=\frac{5}{7}$
Cross-multiplying the terms:
$7(3k-X)=5(4k-X)$
$21k-7X=20k-5X$
Simplifying the terms, we get:
$k=2X$

Next, we are given that the sum of the ages of A and B after $X$ years is 48.
The age of A after $X$ years = $3k+X$
The age of B after $X$ years = $4k+X$
Sum of their ages:
$(3k+X)+(4k+X)=48$
$7k+2X=48$

Substitute $k=2X$ into the equation:
$7\left(2X\right)+2X=48$
$14X+2X=48$
$16X=48$
$X=3$

Now, calculate the value of $k$:
$k=2\left(3\right)=6$

Finally, find the present age of B:
Present age of B = $4k=4\times 6=24$ years.