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

Options

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

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the variables
Let the age of C be represented by \( X \).

### Step 2: Express the ages of B and A in terms of X
Since B is twice as old as C, we can express B's age as:
\[ B = 2X \]

A is two years older than B, so we can express A's age as:
\[ A = B + 2 = 2X + 2 \]

### Step 3: Set up the equation for the total age
According to the problem, the total of the ages of A, B, and C is 27. Therefore, we can write the equation:
\[ A + B + C = 27 \]
Substituting the expressions we have for A, B, and C:
\[ (2X + 2) + (2X) + (X) = 27 \]

### Step 4: Simplify the equation
Combine like terms:
\[ 2X + 2 + 2X + X = 27 \]
This simplifies to:
\[ 5X + 2 = 27 \]

### Step 5: Solve for X
Now, isolate \( X \) by subtracting 2 from both sides:
\[ 5X = 27 - 2 \]
\[ 5X = 25 \]
Now, divide by 5:
\[ X = 5 \]

### Step 6: Find the age of B
Now that we have \( X \), we can find B's age:
\[ B = 2X = 2 \times 5 = 10 \]

### Final Answer
Thus, the age of B is:
\[ \text{B's age} = 10 \text{ years} \]

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