Shyam is 3 times as old as his son. After 10 years the sum of their ages will be 76 years. The respective ages of the father and the son are …… and …… years.

Options

A. 42,14
B. 39,13
C. 45,15
D. None of these

Answer

To solve the problem, we need to find the current ages of Shyam and his son based on the information provided. Let's break it down step by step.

### Step 1: Define Variables
Let the current age of Shyam's son be \( x \) years. Since Shyam is 3 times as old as his son, we can express Shyam's age as \( 3x \) years.

**Hint:** Define variables for the unknowns in the problem to make calculations easier.

### Step 2: Set Up the Equation for Future Ages
According to the problem, after 10 years, the sum of their ages will be 76 years. In 10 years, Shyam's son will be \( x + 10 \) years old, and Shyam will be \( 3x + 10 \) years old. Therefore, we can set up the equation:

\[ (3x + 10) + (x + 10) = 76 \]

**Hint:** Write an equation that represents the future scenario described in the problem.

### Step 3: Simplify the Equation
Now, simplify the equation:

\[ 3x + 10 + x + 10 = 76 \]
\[ 4x + 20 = 76 \]

**Hint:** Combine like terms to simplify the equation.

### Step 4: Solve for \( x \)
Next, we need to isolate \( x \). Start by subtracting 20 from both sides:

\[ 4x = 76 - 20 \]
\[ 4x = 56 \]

Now, divide both sides by 4:

\[ x = \frac{56}{4} \]
\[ x = 14 \]

**Hint:** Perform operations to isolate the variable and solve for it.

### Step 5: Find Shyam's Age
Now that we have \( x \), which is the age of Shyam's son, we can find Shyam's age:

\[ \text{Shyam's age} = 3x = 3 \times 14 = 42 \]

**Hint:** Use the value of \( x \) to find the other unknown variable.

### Conclusion
The respective ages of Shyam and his son are:
- Shyam's age: 42 years
- Son's age: 14 years

**Final Answer:** Shyam is 42 years old and his son is 14 years old.