Final answer:
To find the sum that will amount to rupees 637.50 in 5 years at the same rate of interest, we first calculate the rate of interest from the initial information and then use it in the simple interest formula to solve for the new principal.
Step-by-step explanation:
The question presents a classic scenario of calculating the principal from simple interest, given the amount, rate, and time. First, we will find the rate of interest from the initial information that 450 rupee amounts to rupees 540 in 4 years at simple interest. The interest earned here is 540 - 450 = 90 rupees. Using the formula for simple interest (Interest = Principal × rate × time), we can solve for the rate:
90 = 450 × rate × 4,
rate = (90) / (450 × 4) = 0.05 or 5%.
Now, to find the principal which will amount to 637.50 rupees in 5 years, we will use the same simple interest formula:
Interest = 637.50 - Principal,
and Principal + (Principal × 0.05 × 5) = 637.50.
By solving this equation for Principal, we will get the sum that we need to find.