If Raj was one-third as old as Rahim 5 years back and Raj is 17 years old now, How old is Rahim now?

Options

A. a. 40
B. b. 41
C. c. 36
D. d. 45

Answer

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

### Step-by-Step Solution:

1. **Define the Current Age of Raj**:
- We know that Raj is currently 17 years old.
- Let \( R = 17 \).

2. **Determine Raj's Age 5 Years Ago**:
- To find Raj's age 5 years ago, we subtract 5 from his current age.
- \( R - 5 = 17 - 5 = 12 \).
- So, Raj was 12 years old 5 years ago.

3. **Define the Current Age of Rahim**:
- Let Rahim's current age be \( B \).

4. **Determine Rahim's Age 5 Years Ago**:
- To find Rahim's age 5 years ago, we subtract 5 from his current age.
- \( B - 5 \).

5. **Set Up the Equation Based on the Given Information**:
- According to the problem, 5 years ago, Raj was one-third as old as Rahim.
- This gives us the equation:
\[ R - 5 = \frac{1}{3}(B - 5) \]
- Substituting Raj's age 5 years ago:
\[ 12 = \frac{1}{3}(B - 5) \]

6. **Solve for Rahim's Age**:
- To eliminate the fraction, multiply both sides of the equation by 3:
\[ 12 \times 3 = B - 5 \]
- This simplifies to:
\[ 36 = B - 5 \]
- Now, add 5 to both sides to solve for \( B \):
\[ B = 36 + 5 = 41 \]

7. **Conclusion**:
- Therefore, Rahim's current age is \( 41 \) years.

### Final Answer:
Rahim is currently **41 years old**.

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