Step-by-step Solution:

Quick Solution

Let's represent the ages of Anu, Bhanu, Chanu, and Dhanu as A, B, C, and D respectively. We can solve this by setting up and solving equations from the clues provided.

---

1. Find the Ages of Chanu (C) and Dhanu (D)

We are given two pieces of information about Chanu and Dhanu:

1. Their average age is 19 years: (C + D) / 2 = 19, which means C + D = 38.
2. Dhanu is 10 years older than Chanu: D = C + 10.

We can substitute the second equation into the first to solve for their ages:
C + (C + 10) = 38
2C = 28 => C = 14 years old.
D = 14 + 10 = 24 years old.

---

2. Find the Age of Anu (A)

- The first clue states: A + B = (B + C + D) + 10.
- The age of Bhanu (B) on both sides of the equation cancels out, leaving us with: A = C + D + 10.
- Since we already know that C + D = 38, we can easily find A's age:
A = 38 + 10 = 48 years old.

---

3. Calculate the Final Average Age

- The question asks for the average age of Anu (A) and Dhanu (D).
- Average = (A + D) / 2
- Average = (48 + 24) / 2 = 72 / 2 = 36 years.

---

Final Answer: The average age of Anu and Dhanu is 36 years.