Present age of A is equal to B’s age four years ago. The ratio of the present age of A to that of C is 6:5. If B is 8 years older than C, what B’s present age? (in years)

Options

A. 20
B. 24
C. 28
D. 32

Answer

To solve the problem step by step, we will define the variables and set up equations based on the information given in the question.

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

### Step 2: Set up the first equation
According to the question, the present age of A is equal to B’s age four years ago. This can be expressed as:
\[ A = B - 4 \]
This is our **first equation**.

### Step 3: Set up the second equation
The ratio of the present age of A to that of C is given as 6:5. This can be expressed as:
\[ \frac{A}{C} = \frac{6}{5} \]
Cross-multiplying gives us:
\[ 5A = 6C \]
This can be rearranged to:
\[ A = \frac{6}{5}C \]
This is our **second equation**.

### Step 4: Set up the third equation
It is also given that B is 8 years older than C:
\[ B = C + 8 \]
This is our **third equation**.

### Step 5: Substitute A in terms of B into the second equation
From the first equation, we have \( A = B - 4 \). We can substitute this into the second equation:
\[ B - 4 = \frac{6}{5}C \]

### Step 6: Substitute C in terms of B into the equation
From the third equation, we can express C in terms of B:
\[ C = B - 8 \]
Now substitute this into the equation we derived in Step 5:
\[ B - 4 = \frac{6}{5}(B - 8) \]

### Step 7: Solve for B
Now we will solve the equation:
1. Multiply both sides by 5 to eliminate the fraction:
\[ 5(B - 4) = 6(B - 8) \]
\[ 5B - 20 = 6B - 48 \]
2. Rearranging gives us:
\[ 6B - 5B = 48 - 20 \]
\[ B = 28 \]

### Conclusion
Thus, B's present age is:
\[ \text{B's present age} = 28 \text{ years} \]