The problem asks us to find the principal sum (P) given the total simple interest earned over 9 years with varying interest rates during different periods.

Calculating Total Simple Interest Components

The total simple interest (SI) is the sum of the simple interest earned in each phase.

• Phase 1: First 2 years at 4% per annum. SI$_1$ = $ \frac{P \times 4 \times 2}{100} = \frac{8P}{100} $
• Phase 2: Next 4 years at 6% per annum. SI$_2$ = $ \frac{P \times 6 \times 4}{100} = \frac{24P}{100} $
• Phase 3: Next 3 years at 8% per annum. SI$_3$ = $ \frac{P \times 8 \times 3}{100} = \frac{24P}{100} $

Formulating the Simple Interest Equation

The total simple interest earned is given as ₹ 1120.

Total SI = SI$_1$ + SI$_2$ + SI$_3$

$ 1120 = \frac{8P}{100} + \frac{24P}{100} + \frac{24P}{100} $

Solving for the Principal Sum (P)

Combine the terms on the right side:

$ 1120 = \frac{(8 + 24 + 24)P}{100} $

$ 1120 = \frac{56P}{100} $

Now, isolate P:

$ P = \frac{1120 \times 100}{56} $

Calculate the value:

$ P = \frac{112000}{56} $

$ P = 2000 $

Therefore, the principal sum is ₹ 2000.