Investment Distribution Problem
To solve the problem of investing ₹8829 in three different sectors with equal amounts after specified years at a 4% simple interest rate, we follow these steps:

Understanding Simple Interest
- The formula for calculating simple interest is:
**SI = P × R × T**
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time in years.

Investment Allocation
Let the investments in the three sectors be:
- Sector 1: P1 (for 5 years)
- Sector 2: P2 (for 6 years)
- Sector 3: P3 (for 8 years)
The total investment is given by:
**P1 + P2 + P3 = 8829**

Equal Final Amounts
The final amount for each sector after the respective years can be represented as:
- Final Amount for Sector 1:
**A1 = P1 + SI1 = P1 + (P1 × 4/100 × 5)**
- Final Amount for Sector 2:
**A2 = P2 + SI2 = P2 + (P2 × 4/100 × 6)**
- Final Amount for Sector 3:
**A3 = P3 + SI3 = P3 + (P3 × 4/100 × 8)**
Since A1 = A2 = A3, we can set the equations equal to each other.

Setting the Equations
From the equations, we derive:
- A1 = P1(1 + 0.2) = 1.2P1
- A2 = P2(1 + 0.24) = 1.24P2
- A3 = P3(1 + 0.32) = 1.32P3
Setting these equal gives us:
**1.2P1 = 1.24P2 = 1.32P3**

Solving the Equations
Let:
- P1 = 1.24x
- P2 = x
- P3 = 1.2x
Substituting back into the total investment equation:
**1.24x + x + 1.2x = 8829**
**3.44x = 8829**
**x = 2565**
Finally, calculating each investment:
- P2 = ₹2565
- P1 = ₹3169.6
- P3 = ₹3078
Thus, the amounts invested in each sector ensure they yield equal final amounts after the specified periods.