Given information:
- Three friends Abhilasha, Asaad, and Aditi started a business, each investing rupees 10000.
- After 5 months, Abhilasha withdrew rupees 3000.
- Asaad withdrew rupees 20000.
- Aditi invested rupees 3000 more.
- At the end of the year, there was a total profit of rupees 34600.

Calculating the initial investment:
Since each friend initially invested rupees 10000, the total initial investment would be 10000 * 3 = 30000.

Calculating the adjusted investment after 5 months:
- Abhilasha withdrew rupees 3000 after 5 months, so her adjusted investment would be 10000 - 3000 = 7000.
- Asaad did not withdraw any amount, so his adjusted investment would remain 10000.
- Aditi invested an additional rupees 3000, so her adjusted investment would be 10000 + 3000 = 13000.

Calculating the profit distribution:
Let's assume Abhilasha's share of the profit as A, Asaad's share as B, and Aditi's share as C.

- Abhilasha's profit share would be (A / 30000) * 7000.
- Asaad's profit share would be (B / 30000) * 10000.
- Aditi's profit share would be (C / 30000) * 13000.

The sum of their profit shares should be equal to the total profit of rupees 34600.

Therefore, we can write the equation as A + B + C = 34600.

Calculating individual profit shares:
To calculate the individual profit shares, we need to solve the equation and find the values of A, B, and C.

- From the given information, we know that A = (B / 30000) * 10000 - 3000.
- Substituting the value of A in the equation, we get (B / 30000) * 10000 - 3000 + B + C = 34600.
- Simplifying the equation, we get (4B + 3C) / 10 = 37600.
- Multiplying both sides of the equation by 10, we get 4B + 3C = 376000.

Using trial and error method:
Now, we can use the trial and error method to find the values of B and C that satisfy the equation.

Let's assume B = 10000 and C = 30000.

- Substituting the values in the equation, we get 4 * 10000 + 3 * 30000 = 40000 + 90000 = 130000.
- As the obtained value is greater than the expected value (376000), we can conclude that the assumed values are incorrect.

We can repeat the trial and error method with different values of B and C until we find the values that satisfy the equation.

Conclusion:
Using the trial and error method, we can find the values of B and C that satisfy the equation. Once we have the values of B and C, we can calculate A using the equation A = (B / 30000)