A certain principal earns a simple interest of Rs 2260 in 3 years at some unknown rate of interest. If the rate of interest per annum had been 1% higher than the actual rate, by how much additional simple interest would the amount have increased over the same period of 3 years, or can this not be uniquely determined from the given data?

Introduction / Context:
This question tests your understanding of the relationship between principal, rate, time, and interest in simple interest problems. It also focuses on whether the given data are sufficient to compute a unique numerical answer. Many aptitude questions are designed to see if you correctly identify that there are too many unknowns compared to the number of equations provided.

Given Data / Assumptions:

A principal amount P earns simple interest of Rs 2260 in 3 years.
The rate of interest per annum is r%, which is not directly given.
Simple interest formula: SI = (P * r * T) / 100.
Time T in this problem is 3 years.
We are asked to consider what happens if the rate becomes (r + 1)% per annum for the same 3 years and to find the additional interest or decide if it cannot be uniquely determined.

Concept / Approach:
From the given information, we can form one equation involving P and r using the simple interest formula. However, there are two unknowns and only one equation, so P and r individually cannot be obtained. To find the extra interest when the rate increases by 1%, we need the value of P. Since P depends on both r and the known interest, and r is unknown, there will be infinitely many possible values for P that satisfy the equation. Therefore the additional interest cannot be uniquely fixed.

Step-by-Step Solution:
Step 1: Use SI = (P * r * T) / 100 with SI = 2260 and T = 3. Step 2: 2260 = (P * r * 3) / 100. Step 3: Rearranging gives P * r = (2260 * 100) / 3. Step 4: Thus, P * r is known numerically, but P alone and r alone are not known. Step 5: If the rate were (r + 1)%, the new simple interest in 3 years would be SI_new = (P * (r + 1) * 3) / 100. Step 6: The additional interest would be SI_new - SI_original = (P * 3 / 100) * (r + 1 - r) = (3P) / 100. Step 7: To compute (3P) / 100 exactly, we need P. However, we only know P * r, not P. Step 8: Different combinations of P and r can give the same product P * r, so multiple answers for the extra interest are possible.

Verification / Alternative check:
Assume some trial value of r that satisfies the original equation and compute P from P = (2260 * 100) / (3 * r). For a different value of r that also satisfies the equation, a different P will result, giving a different value of (3P) / 100. This shows there is no single unique amount for the additional interest, confirming that the data are insufficient.

Why Other Options Are Wrong:
Any numerical option such as Rs 175, Rs 220.75, Rs 126, or Rs 150 assumes a specific fixed principal, which is not determined by the information given. Since P is not uniquely determined, none of these fixed values can be guaranteed to be correct in every consistent scenario. Hence, all numerical options are unjustified.

Common Pitfalls:
A common mistake is to try to assume a convenient rate and principal without realizing that many different combinations satisfy the original simple interest equation. Another error is to treat P * r as if it directly gives P or r. Always check the number of independent equations versus the number of unknowns before concluding you have a unique answer.

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