The average value of the property owned by Agil, Mugilan and Anitha is Rs. 130 crore. Agil's property value is Rs. 20 crore more than Mugilan's property value, and Anitha's property value is Rs. 50 crore more than Agil's property value. What is the value of Anitha's property?

Introduction / Context:
This is an averages and linear equations question based on three related quantities. We know the average property value of three people and the differences between their individual property values. Using this information, we can set up algebraic equations to determine each person's property value and specifically find Anitha's share.

Given Data / Assumptions:
Average property value of Agil, Mugilan and Anitha is Rs. 130 crore.Therefore, the total combined property value is 3 × 130 = Rs. 390 crore.Let Mugilan's property value be M crore.Agil's property value is Rs. 20 crore more than Mugilan's, so Agil's property is M + 20 crore.Anitha's property value is Rs. 50 crore more than Agil's property value.

Concept / Approach:
We express all three property values in terms of Mugilan's property M. Then we use the total property value based on the average to form an equation in M. Solving this equation gives M, after which we compute Agil's and Anitha's property values using the given differences.

Step-by-Step Solution:
Step 1: Write Mugilan's property as M.Step 2: Agil's property is M + 20.Step 3: Anitha's property is 50 more than Agil's, so Anitha's property is (M + 20) + 50 = M + 70.Step 4: Total property value of all three is M + (M + 20) + (M + 70) = 3M + 90.Step 5: From the given average, total property is 3 × 130 = 390.Step 6: Set up the equation: 3M + 90 = 390.Step 7: Subtract 90 from both sides: 3M = 300.Step 8: Divide both sides by 3: M = 100.Step 9: Agil's property is M + 20 = 100 + 20 = 120.Step 10: Anitha's property is M + 70 = 100 + 70 = 170.

Verification / Alternative check:
Check the totals. With Mugilan at 100, Agil at 120 and Anitha at 170, the total property is 100 + 120 + 170 = 390 crore. Dividing by 3 gives an average of 130 crore, which matches the given information. Anitha's property is indeed Rs. 50 crore more than Agil's and Agil's is Rs. 20 crore more than Mugilan's, confirming that the relationships are satisfied.

Why Other Options Are Wrong:
If Anitha had 120 crore, the differences with the others could not satisfy the given relationships and the average would not be 130 crore. Similarly, 100 crore or 150 crore for Anitha lead to totals that do not equal 390 crore with the stated differences. Only 170 crore fits both the average and the difference conditions.

Common Pitfalls:
Common mistakes include misinterpreting which person has more property and by how much, or setting up the total incorrectly. Some may forget to multiply the average by the number of people to get the total. Properly labelling each person's property in terms of a single variable avoids confusion.

Final Answer:
The value of Anitha's property is Rs. 170 crore.