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's solve the problem step-by-step to find the present age of B.

Step 1: Express the present ages of A and B using a constant.
The ratio of present ages of A to B is given as 3 : 4.
Let the present age of A be $3k$ years.
Let the present age of B be $4k$ years.

Step 2: Use the condition for ages X years ago.
X years ago:
Age of A = $3k-X$
Age of B = $4k-X$

The ratio of their ages X years ago was 5 : 7. So, we can set up the equation:

$\frac{3k-X}{4k-X}=\frac{5}{7}$

Cross-multiplying to simplify the equation:
$7(3k-X)=5(4k-X)$
$21k-7X=20k-5X$
$21k-20k=7X-5X$
$k=2X$ --- (Equation 1)

Step 3: Use the condition for the sum of ages after X years.
After X years:
Age of A = $3k+X$
Age of B = $4k+X$

The sum of their ages after X years is 48:
$(3k+X)+(4k+X)=48$
$7k+2X=48$ --- (Equation 2)

Step 4: Solve for k and X.
From Equation 1, we know that $2X=k$. Substitute this into Equation 2:
$7k+k=48$
$8k=48$
$k=6$

Step 5: Calculate the present age of B.
The present age of B is $4k$.
Present age of B = $4\times 6=24$ years.

Thus, the present age of B is 24 years.