A is three times as old as B. C was twice as old as A four years before. In four years' times A will be 31. What are the present ages of B and C?

Options

A. 9,46
B. 9,50
C. 10,46
D. 10,50

Explanation

To solve the problem step by step, we will define the variables and use the information given in the question to form equations.

### Step 1: Define the variables
Let:
- A = present age of A
- B = present age of B
- C = present age of C

### Step 2: Set up the equations based on the information given
1. From the statement "A is three times as old as B", we can write:
\[ A = 3B \quad \text{(Equation 1)} \]

2. The statement "C was twice as old as A four years before" can be expressed as:
\[ C - 4 = 2(A - 4) \quad \text{(Equation 2)} \]

3. The statement "In four years' time A will be 31" gives us:
\[ A + 4 = 31 \]
From this, we can solve for A:
\[ A = 31 - 4 = 27 \quad \text{(Equation 3)} \]

### Step 3: Substitute the value of A into Equation 1
Now we will substitute \( A = 27 \) into Equation 1:
\[ 27 = 3B \]
To find B, we divide both sides by 3:
\[ B = \frac{27}{3} = 9 \quad \text{(Age of B)} \]

### Step 4: Substitute the value of A into Equation 2 to find C
Now we substitute \( A = 27 \) into Equation 2:
\[ C - 4 = 2(27 - 4) \]
Calculating the right side:
\[ C - 4 = 2(23) = 46 \]
Now, solving for C:
\[ C = 46 + 4 = 50 \quad \text{(Age of C)} \]

### Final Answer
Thus, the present ages are:
- Present age of B = 9 years
- Present age of C = 50 years