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 option is 24 years.

Let us solve the problem step-by-step to find the present age of B.

Step 1: Define variables for the present ages of A and B
The ratio of the present ages of A to B is given as 3:4.
Therefore, we can represent their present ages as:
Present age of A = $3k$
Present age of B = $4k$
where $k$ is a constant multiplier.

Step 2: Use the sum of their ages after X years
We are given that the sum of the ages of A and B after $X$ years is 48.
Age of A after $X$ years = $3k+X$
Age of B after $X$ years = $4k+X$
According to the problem:
$(3k+X)+(4k+X)=48$
Simplifying this equation:
$7k+2X=48$ --- (Equation 1)

Step 3: Use the ratio of their ages X years ago
The ratio of their ages $X$ years ago was 5:7.
Age of A, $X$ years ago = $3k-X$
Age of B, $X$ years ago = $4k-X$
According to the problem:
$\frac{3k-X}{4k-X}=\frac{5}{7}$
Cross-multiplying to simplify:
$7(3k-X)=5(4k-X)$
$21k-7X=20k-5X$
$21k-20k=7X-5X$
$k=2X$ --- (Equation 2)

Step 4: Solve for k
Substitute the value of $2X$ from Equation 2 into Equation 1:
$7k+k=48$
$8k=48$
$k=6$

Step 5: Calculate the present age of B
Present age of B = $4k$
$4\times 6=24\text{years}$

Thus, the present age of B is 24 years.