Rahim’s father is three times as old as Rahim. If sum of their ages is `56` years, find their ages.

Options

A. Rahim’s age = `14`yrs

His father’s age = `40` yrs
B. Rahim’s age = `12`yrs

His father’s age = `42` yrs
C. Rahim’s age = `14`yrs

His father’s age = `42` yrs
D. Rahim’s age = `12`yrs

His father’s age = `40` yrs

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Variables
Let Rahim's age be represented by \( x \) years.

### Step 2: Express Father's Age
Since Rahim’s father is three times as old as Rahim, we can express his age as \( 3x \) years.

### Step 3: Set Up the Equation
According to the problem, the sum of their ages is 56 years. Therefore, we can write the equation:
\[ x + 3x = 56 \]

### Step 4: Simplify the Equation
Combine like terms:
\[ 4x = 56 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides of the equation by 4:
\[ x = \frac{56}{4} \]
\[ x = 14 \]

### Step 6: Find Rahim's Father's Age
Now that we have Rahim's age, we can find his father's age:
\[ \text{Father's age} = 3x = 3 \times 14 = 42 \]

### Conclusion
Rahim's age is \( 14 \) years, and his father's age is \( 42 \) years.

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