Final answer:
To find the principal sum with simple interest, we can use the given information along with the interest rate of 5% p.a. Statements I and II each provide enough information when combined with the interest rate from statement III to determine the principal sum. Thus, any two of the three statements are sufficient to find the principal, making option D the correct choice.
Step-by-step explanation:
To find the principal sum in a situation involving simple interest, we can use the formula for simple interest which is I = PRT, where I is the interest, P is the principal sum, R is the rate of interest per annum, and T is the time in years. Given that the rate of interest is 5% p.a., we can align the given information to find out the principal.
Using statement I: P + (P × 0.05 × 3) = Rs. 690. Simplifying this, we get P + 0.15P = 690, hence 1.15P = 690. Solving for P gives us the principal sum for statement I.
Using statement II: P + (P × 0.05 × 5) = Rs. 750. Simplifying, we get P + 0.25P = 750, so 1.25P = 750. Solving for P gives the principal sum for statement II.
Now, by using either statement I or II along with statement III, we can determine the principal. It is not necessary to use all three statements together as each of the first two statements combined with the interest rate is sufficient to find the principal amount.
Therefore, the correct option answer in the final answer is option D) Any two of the three statements are sufficient to answer the question.