Let's solve this problem step-by-step.

The problem states:

1. Chagan is 5 years older than Raman.
2. Raman is three times older than Mahesh.
3. The sum of their ages is 47 years.
4. We need to find Chagan's age.

Let's define:

• Mahesh's age as $M$
• Raman's age as $R$
• Chagan's age as $C$

Step 1: Translate the conditions into equations

1. Raman's age is three times Mahesh's age: $R = 3M$

2. Chagan is 5 years older than Raman: $C = R + 5$

3. The sum of their ages is 47 years: $C + R + M = 47$

Step 2: Substitute the values

Using $R = 3M$ in the sum equation: $C + 3M + M = 47$ $C + 4M = 47$

Now, substitute $C = 3M + 5$ into the equation: $3M + 5 + 4M = 47$ $7M + 5 = 47$ $7M = 42$ $M = 6$

Step 3: Calculate $R$ and $C$

• Since $M = 6$: $R = 3 \times 6 = 18$ $C = 18 + 5 = 23$

Conclusion

Chagan's age is 23 years.

Answer:

The correct option is: (C) 23 years

Would you like a breakdown of any step or more clarification?

1. What would happen if the total age was different?
2. How do we find Mahesh's age if we only know Chagan's and Raman's relationship?
3. Can you explain the substitution method used here?
4. What if Raman’s age was four times Mahesh's age?
5. How can we set up similar equations for different relationships?

Tip: In age-related problems, always start by assigning variables and forming equations based on relationships.