At present, A is younger than B by 8 years. If 4 years ago, their ages were in the ratio 1 : 2, then what is the present age of B (in years)?

The correct option is 20.

To find the present age of B, we can translate the information given in the question into algebraic equations step-by-step.

Step 1: Define the variables for their present ages
Let the present age of B be represented by $x$ years.
Since A is younger than B by 8 years, the present age of A can be represented as:

$\mathrm{Present\; age\; of\; A}=x-8$

Step 2: Determine their ages 4 years ago
To find their ages 4 years ago, we subtract 4 from their present ages:
Age of B 4 years ago:

$x-4$

Age of A 4 years ago:

$(x-8)-4=x-12$

Step 3: Use the ratio given for their ages 4 years ago
We are given that 4 years ago, the ratio of A's age to B's age was 1 : 2. We can set up the following equation:

$\frac{x-12}{x-4}=\frac{1}{2}$

Step 4: Solve the equation for $x$
Cross-multiply to eliminate the fractions:

$2(x-12)=1(x-4)$

Distribute the terms on both sides:

$2x-24=x-4$

Subtract $x$ from both sides of the equation:

$x-24=-4$

Add 24 to both sides to solve for $x$:

$x=-4+24$

$x=20$

Thus, the present age of B is 20 years.