The sum of Ravi's and Shivam's age 4 years ago was 80 years. Ravi's age 14 years ago was equal to Shivam's age 4 years ago, then find the present age of Ravi ? (in years)

Options

A. A)39
B. B)49
C. C)40
D. D)47

Answer

To solve the problem step by step, we will denote Ravi's present age as \( R \) and Shivam's present age as \( S \).

### Step 1: Set up the equations based on the information given.
1. **Four years ago**, Ravi's age was \( R - 4 \) and Shivam's age was \( S - 4 \).
2. According to the problem, the sum of their ages four years ago was 80 years:
\[ (R - 4) + (S - 4) = 80 \]
Simplifying this gives:
\[ R + S - 8 = 80 \implies R + S = 88 \quad \text{(Equation 1)} \]

### Step 2: Set up the second equation based on the age relationship.
3. The problem states that Ravi's age 14 years ago was equal to Shivam's age 4 years ago:
\[ R - 14 = S - 4 \]
Rearranging this gives:
\[ R - S = 10 \quad \text{(Equation 2)} \]

### Step 3: Solve the system of equations.
4. Now we have two equations:
- Equation 1: \( R + S = 88 \)
- Equation 2: \( R - S = 10 \)

5. We can add these two equations:
\[ (R + S) + (R - S) = 88 + 10 \]
This simplifies to:
\[ 2R = 98 \]
Dividing both sides by 2 gives:
\[ R = 49 \]

### Step 4: Conclusion.
6. Therefore, the present age of Ravi is \( R = 49 \) years.