A certain sum of money earns Rs. 1,750 as simple interest in 7 years at a certain rate of interest. Had the rate been 2% per annum more, how much additional interest would the sum have earned in those 7 years?

Introduction / Context:
This question looks like a regular simple interest problem but is actually testing whether you notice that the given information is insufficient to determine a unique numerical answer. In many aptitude exams, some questions are designed to see if you correctly recognize when data is incomplete and therefore the result cannot be uniquely determined.

Given Data / Assumptions:

• Total simple interest earned = Rs. 1,750
• Time period = 7 years
• Rate of interest = r percent per annum (unknown)
• If the rate were increased by 2% (that is, to r + 2), we are asked to find the extra interest earned

Concept / Approach:
For simple interest, the formula is:
SI = (P * R * T) / 100Let P be the principal and r be the original rate. From the given information, we can write:
(P * r * 7) / 100 = 1750This equation links P and r but does not give a unique value for either. The extra interest if the rate is increased by 2% would depend only on the principal and the time, but we still need the principal to calculate the exact amount.

Step-by-Step Solution:
From (P * r * 7) / 100 = 1750, we get P * r = (1750 * 100) / 7P * r = 25000Extra rate = 2% per annumExtra interest over 7 years = (P * 2 * 7) / 100 = (14P) / 100However, we do not know P directly. The equation P * r = 25000 shows that different combinations of P and r are possible. For each different P and r that satisfy this product, the value of (14P) / 100 changes. Therefore the extra interest cannot be uniquely found.

Verification / Alternative check:
Suppose r is 5%. Then P would be 25000 / 5 = Rs. 5,000 and extra interest would be 14 * 5000 / 100 = Rs. 700. If r is 10%, then P would be 2500 and extra interest would be 14 * 2500 / 100 = Rs. 350. We already see two different possible extra interests (700 and 350), both consistent with the original data. This proves that the answer is not unique.

Why Other Options Are Wrong:
The numerical options Rs. 35, Rs. 245 and Rs. 350 each correspond to specific choices of principal and rate. Since many such combinations are possible, no single numerical option can always be correct. Only the option stating that the answer cannot be determined is consistent with the information.

Common Pitfalls:
Candidates often attempt to force a numerical answer by assuming some specific value of the rate without justification. Another common mistake is to think that the extra interest must be a fixed proportion of the given simple interest. In reality, without principal or rate separately, the extra interest cannot be fixed.

Final Answer:
The additional interest cannot be uniquely found from the given data, so the correct choice is cannot be determined.