Final answer:
To solve for the principal and the annual interest rate, we use the simple interest formula and data provided for the amounts after 3 and 5 years. We calculate the interest for the two periods and find the difference to establish a system of equations that can be solved to get the required values.
Step-by-step explanation:
To find the sum and the rate percent per annum for a certain amount of rupees that increases at a simple interest over a period of time, we use the formula for calculating simple interest: Simple Interest (SI) = Principal (P) × Rate (R) × Time (T) and the formula for total amount: Total Amount = Principal + Simple Interest.
According to the question, we have two scenarios:
- The total amount after 3 years is 5960 rupees.
- The total amount after 5 years is 6916 rupees.
We calculate the simple interest for the 3-year period and the 5-year period, and the difference between these two interests gives us the simple interest for the 2-year period.
Let the principal amount be P and the rate per annum be R%.
Using the data from the 3-year and 5-year periods, we apply the simple interest formula to solve for P and R.
Working through the math, we eventually find the principal amount and the annual interest rate that matches the given conditions for the amounts after 3 and 5 years. The detailed steps would involve setting up and solving a system of equations based on the simple interest formula.