Althaf borrows a total of Rs 1500 from two moneylenders under simple interest. One part of the loan carries 12% per annum and the remaining part carries 14% per annum for one full year. If the total interest he pays for that year is Rs 186, how much of the original amount was borrowed at 12% per annum using the simple interest formula?

Introduction / Context:
This aptitude question tests understanding of the simple interest formula when a total principal is split into two parts that earn different rates of interest. The learner needs to express the total interest as the sum of interests on each part and then form a linear equation in one variable. Such problems are common in bank exam quantitative aptitude sections and help build confidence with algebraic representation of real life borrowing situations.

Given Data / Assumptions:

• Total amount borrowed by Althaf = Rs 1500.
• One part of the money is borrowed at 12% simple interest per annum.
• The remaining part is borrowed at 14% simple interest per annum.
• Time period for both loans = 1 year.
• Total interest paid after 1 year = Rs 186.
• Interest is calculated using simple interest throughout.

Concept / Approach:
For simple interest, the formula is:
Simple interest = (Principal * Rate * Time) / 100 Here the total principal is split into two parts, say x and 1500 − x. Each part earns interest at its own rate for the same time. The total interest is the sum of the two simple interests. By equating this total to the given interest (Rs 186), we obtain a linear equation in x. Solving that equation gives the amount borrowed at 12% per annum.

Step-by-Step Solution:
Let the amount borrowed at 12% per annum be x rupees. Then the amount borrowed at 14% per annum is 1500 − x rupees. Simple interest on the first part for 1 year = (x * 12 * 1) / 100 = 0.12x. Simple interest on the second part for 1 year = ((1500 − x) * 14 * 1) / 100 = 0.14 * (1500 − x). Total interest for 1 year = 0.12x + 0.14 * (1500 − x). Given total interest = Rs 186, so 0.12x + 0.14 * (1500 − x) = 186. 0.12x + 210 − 0.14x = 186. −0.02x + 210 = 186. −0.02x = 186 − 210 = −24. x = (−24) / (−0.02) = 1200. Therefore, the amount borrowed at 12% per annum is Rs 1200.

Verification / Alternative check:
If Rs 1200 is borrowed at 12% for 1 year, interest = (1200 * 12 * 1) / 100 = Rs 144. The remaining Rs 300 is borrowed at 14%, so interest = (300 * 14 * 1) / 100 = Rs 42. Total interest = 144 + 42 = Rs 186, which matches the given information. Hence the solution is consistent and correct.

Why Other Options Are Wrong:
Rs 300 would give very small interest at 12% and would not produce the required total of Rs 186 when combined with the remaining part at 14%.
Rs 400 also fails to satisfy the total interest equation when calculated precisely.
Rs 1100 produces a total interest that is less than or greater than Rs 186 when checked with both rates.
Rs 900 similarly does not give a total interest of Rs 186 for the given rates and period.

Common Pitfalls:
Students sometimes assume equal division of the principal between the two rates, which is not given in this question. Another common mistake is to forget that the time period is the same for both loans and accidentally multiply by different time values. Some learners also directly divide the difference in rates into the total interest without forming the correct equation, which leads to wrong values. Careful setup of the equation and systematic simplification prevent such errors.

Final Answer:
Thus, the amount of the loan that was borrowed at 12% simple interest per annum is Rs 1200.