Problem Breakdown: Average Age Calculation

We need to find Chitra's age three years ago based on the given average ages at different points in time.

Step 1: Calculate the sum of current ages (Amit, Bharat, Chitra)

Four years ago, the average age of Amit, Bharat, and Chitra was 36 years.

• Ages four years ago: $(A-4), (B-4), (C-4)$
• Sum of ages four years ago: $(A-4) + (B-4) + (C-4) = 3 \times 36 = 108$
• This simplifies to: $A + B + C - 12 = 108$
• Therefore, the sum of their current ages is: $A + B + C = 108 + 12 = 120$ years.

Step 2: Calculate the sum of current ages (Amit, Bharat)

Six years ago, the average age of Amit and Bharat was 30 years.

• Ages six years ago: $(A-6), (B-6)$
• Sum of ages six years ago: $(A-6) + (B-6) = 2 \times 30 = 60$
• This simplifies to: $A + B - 12 = 60$
• Therefore, the sum of their current ages is: $A + B = 60 + 12 = 72$ years.

Step 3: Calculate Chitra's current age

Using the sums calculated above:

• We know $A + B + C = 120$.
• We also know $A + B = 72$.
• Substituting the value of $(A+B)$ into the first equation: $72 + C = 120$.
• Solving for Chitra's current age (C): $C = 120 - 72 = 48$ years.

Step 4: Calculate Chitra's age three years ago

Chitra's current age is 48 years.

• Chitra's age three years ago = Current Age - 3
• Chitra's age three years ago = $48 - 3 = 45$ years.

The age of Chitra three years ago was 45 years.