A is 2 years older than B who is twice as old as C. If the total of the ages of A, B and C be 27 years, then how old is B?

Options

A. 7 years
B. 8 years
C. 9 years
D. 10 years

Answer

To solve the problem step by step, we will define the ages of A, B, and C using algebraic expressions based on the information given in the question.

### Step 1: Define the variables
Let:
- The age of C be \( x \).
- Since B is twice as old as C, the age of B will be \( 2x \).
- A is 2 years older than B, so the age of A will be \( 2x + 2 \).

### Step 2: Set up the equation
According to the problem, the total of the ages of A, B, and C is 27 years. Therefore, we can write the equation:
\[ A + B + C = 27 \]
Substituting the expressions we defined:
\[ (2x + 2) + (2x) + (x) = 27 \]

### Step 3: Simplify the equation
Now, combine like terms:
\[ 2x + 2 + 2x + x = 27 \]
This simplifies to:
\[ 5x + 2 = 27 \]

### Step 4: Solve for \( x \)
Next, we will isolate \( x \) by subtracting 2 from both sides:
\[ 5x = 27 - 2 \]
\[ 5x = 25 \]
Now, divide both sides by 5:
\[ x = \frac{25}{5} = 5 \]

### Step 5: Find the age of B
Now that we have the value of \( x \), we can find the age of B:
\[ B = 2x = 2 \times 5 = 10 \]

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

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