Final answer:
By finding the yearly interest from the given amounts for 3 and 4 years, we can calculate the principal sum to be Rupees 698. This sum is found through simple subtraction and represents the initial amount before interest, corresponding to option (c).
Step-by-step explanation:
The student's question is related to finding the principal sum of money that amounts to Rs. 815 in 3 years and Rs. 854 in 4 years at a certain simple interest rate. Let's denote the principal sum as P, the interest earned per year as I, and the simple interest rate as R. As the amount increases by Rs. 854 - Rs. 815 = Rs. 39 in one year, this is the simple interest for one year. Hence, we have:
- 815 = P + (3 * I)
- 854 = P + (4 * I)
Subtract the first equation from the second to find I:
854 - 815 = 39 = I
Substituting I back into the first equation gives us:
815 = P + (3 * 39)
815 = P + 117
P = 815 - 117
P = 698
Therefore, the principal sum is Rupees 698, which corresponds to option (c).