**Solution:**

Given,

- Sum of money amounts to Rs. 20800 in 5 years
- Sum of money amounts to Rs. 22720 in 7 years

Let the principal be 'P' and rate of interest be 'R'.

### Finding the Interest

Using the formula,

`Simple Interest = (P * R * T)/100`

Where,

- P = Principal
- R = Rate of Interest
- T = Time

We can find the interest earned by the principal in 2 years as follows:

- Interest earned in 5 years = (P * R * 5)/100
- Interest earned in 7 years = (P * R * 7)/100

Subtracting the above two equations, we get:

- (P * R * 7)/100 - (P * R * 5)/100 = 22720 - 20800
- (P * R * 2)/100 = 1920
- PR = 96000

### Finding the Principal

Using the formula,

`Amount = P + SI`

Where,

- P = Principal
- SI = Simple Interest

We can find the principal as follows:

- Amount after 5 years = P + (P * R * 5)/100
- Amount after 7 years = P + (P * R * 7)/100

Subtracting the above two equations, we get:

- P + (P * R * 7)/100 - P - (P * R * 5)/100 = 22720 - 20800
- (P * R * 2)/100 = 1920
- PR = 96000

Substituting the value of PR in any of the above equations, we get:

- P + (96000 * R * 5)/100 = 20800
- P + 4800R = 20800

Substituting the value of R from the equation PR = 96000, we get:

- P + 4800 * (96000/P) = 20800
- P^2 - 10400P + 96000 = 0

Solving the above quadratic equation, we get:

- P = 8000 or P = 12000

### Conclusion

Therefore, the principal is Rs. 8000 or Rs. 12000 and the rate of interest is 12.5%.

16000,6%