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?

Options

A. 10
B. 11
C. 12
D. 13

Explanation

To solve the problem step by step, we will define the ages of A, B, C, and D using variables and then use the information given in the question to find the age of B.

### Step 1: Define the variables
Let:
- Age of A = a
- Age of B = b
- Age of C = c
- Age of D = d

### Step 2: Write down the relationships from the question
1. A is 3 years younger than C:
\( a = c - 3 \)

2. A is 1 year older than D:
\( a = d + 1 \)

3. D is 1 year older than B:
\( d = b + 1 \)

4. D is 4 years younger than C:
\( d = c - 4 \)

5. C is 15 years old:
\( c = 15 \)

### Step 3: Substitute the value of C into the equations
From the fifth equation, substitute \( c = 15 \) into the first equation:
\( a = 15 - 3 = 12 \)
So, the age of A is 12 years.

### Step 4: Find the age of D
Now, substitute the age of A into the second equation:
\( 12 = d + 1 \)
This gives us:
\( d = 12 - 1 = 11 \)
So, the age of D is 11 years.

### Step 5: Find the age of B
Now, substitute the age of D into the third equation:
\( 11 = b + 1 \)
This gives us:
\( b = 11 - 1 = 10 \)
So, the age of B is 10 years.

### Conclusion
Thus, the age of B is 10 years.