A is 3 years younger than C but one year older than D. D is one year older than B but 4 years younger than C. C is 15 years old. What is the age of B in years?

The correct option is 10.

We are given the following relationships between the ages of A, B, C, and D:

1. C is 15 years old.
2. A is 3 years younger than C.
3. A is 1 year older than D.
4. D is 1 year older than B.
5. D is 4 years younger than C.

Let us determine the ages step-by-step starting with C's age:

First, we know C's age directly:

$C=15$

Next, we calculate A's age. Since A is 3 years younger than C, we subtract 3 from C's age:

$A=C-3$

Substituting C = 15:

$A=15-3=12$

Now, we find D's age. We are told that A is 1 year older than D. Therefore, D is 1 year younger than A:

$D=A-1$

Substituting A = 12:

$D=12-1=11$

We can verify D's age using the second condition, which states that D is 4 years younger than C:

$D=C-4=15-4=11$

Both methods yield the same age of 11 for D, confirming our calculations are correct so far.

Finally, we calculate B's age. Since D is 1 year older than B, B must be 1 year younger than D:

$B=D-1$

Substituting D = 11:

$B=11-1=10$

Thus, the age of B is 10 years.