A is 5 times as old as his son B. Four years hence the sum of their ages will be 50 years. B’s age now is

Options

A. 8 years
B. 6 years
C. 7 years
D. 5 years

Answer

To solve the problem, let's break it down step by step.

### Step 1: Define the Variables
Let the current age of B (the son) be \( x \). Since A is 5 times as old as B, we can express A's age as:
\[ A = 5x \]

### Step 2: Determine Their Ages in Four Years
In four years, B's age will be:
\[ B's \, age \, in \, 4 \, years = x + 4 \]
And A's age will be:
\[ A's \, age \, in \, 4 \, years = 5x + 4 \]

### Step 3: Set Up the Equation
According to the problem, the sum of their ages in four years will be 50 years. Therefore, we can write the equation:
\[ (x + 4) + (5x + 4) = 50 \]

### Step 4: Simplify the Equation
Now, simplify the equation:
\[ x + 4 + 5x + 4 = 50 \]
Combine like terms:
\[ 6x + 8 = 50 \]

### Step 5: Solve for \( x \)
Subtract 8 from both sides:
\[ 6x = 50 - 8 \]
\[ 6x = 42 \]
Now, divide both sides by 6:
\[ x = \frac{42}{6} \]
\[ x = 7 \]

### Step 6: Conclusion
Thus, B's current age is:
\[ \text{B's age now} = 7 \, \text{years} \]