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. If the total interest he pays for one full year is Rs. 186, how much of the amount was borrowed at 12% per annum?

Introduction / Context:
This problem is based on simple interest and on splitting a total borrowed amount into two parts that are invested or borrowed at different rates of interest. Many banking and finance aptitude questions test whether a learner can convert such a word problem into a linear equation in one variable and then solve it accurately. Here Althaf borrows a fixed total sum from two moneylenders, each charging a different annual simple interest rate, and the total interest for one year is given. Our goal is to determine how much of the principal was taken at the lower rate of 12 percent per annum.

Given Data / Assumptions:
Total amount borrowed is Rs. 1500.
One part is borrowed at 12 percent simple interest per annum.
The remaining part is borrowed at 14 percent simple interest per annum.
The time period is one year.
Total interest paid at the end of one year is Rs. 186.
Interest is calculated using the simple interest formula with a constant rate over the year.

Concept / Approach:
For simple interest, the formula is:
Simple interest = Principal * Rate * Time / 100.
When a total sum is split into two parts with different rates, we represent one part as a variable and the other as total minus that variable. We then compute the interest from each part and add them. The sum of these two interests is equated to the given total interest. Solving this linear equation gives the principal borrowed at one of the rates. This equation approach is standard in mixture of interest rate questions.

Step-by-Step Solution:
Let the amount borrowed at 12 percent per annum be x rupees.Then the amount borrowed at 14 percent per annum is 1500 - x rupees.Interest from the 12 percent part for one year is x * 12 * 1 / 100 = 0.12x rupees.Interest from the 14 percent part for one year is (1500 - x) * 14 * 1 / 100 = 0.14 * (1500 - x) rupees.Total interest for one year is given as 186 rupees, so we write 0.12x + 0.14 * (1500 - x) = 186.Expand the second term: 0.12x + 0.14 * 1500 - 0.14x = 186.Compute 0.14 * 1500 = 210, so we get 0.12x + 210 - 0.14x = 186.Combine like terms for x: (0.12 - 0.14)x + 210 = 186 which gives -0.02x + 210 = 186.Rearrange to -0.02x = 186 - 210 = -24.So x = -24 / -0.02 = 1200 rupees.Thus the amount borrowed at 12 percent per annum is Rs. 1200.

Verification / Alternative check:
If Althaf borrows Rs. 1200 at 12 percent and Rs. 300 at 14 percent, then interest from the first part is 1200 * 12 / 100 = 144 rupees and from the second part is 300 * 14 / 100 = 42 rupees. Adding them gives 144 + 42 = 186 rupees, which matches the given total interest. Therefore, the computed split of the loan is consistent and verifies the solution.

Why Other Options Are Wrong:
Rs. 300 would give very small interest at 12 percent and would not add up to 186 rupees when combined with interest from the remaining amount at 14 percent.
Rs. 400 similarly leads to a total interest lower than 186 rupees when both parts are evaluated.
Rs. 1100 results in a mismatched total because the interest from 1100 at 12 percent plus interest on 400 at 14 percent does not equal 186 rupees.
Rs. 900 is another arbitrary split that fails when the simple interest is calculated and summed for both parts.

Common Pitfalls:
Students sometimes interchange the rates or mistakenly assume equal halves of the principal at both rates. Another frequent error is to forget that the time period is the same for both parts, which is crucial for forming a single equation. Errors in handling decimal coefficients such as 0.12 and 0.14 can also lead to incorrect results. Writing the total interest equation correctly and simplifying carefully is essential to avoid arithmetic mistakes.

Final Answer:
The amount that Althaf borrows at the rate of 12 percent simple interest per annum is Rs. 1200.