Rs 1,500 is divided into two parts such that if one part is invested at 6% per annum and the other part at 5% per annum, the total annual simple interest from both parts is Rs 85. How much money was invested at 5% per annum?

Introduction / Context:
This question involves splitting a fixed amount into two parts and investing them at different simple interest rates such that the total yearly interest is known. Your task is to determine how much was placed at the lower rate. It is a linear equation problem combined with a simple interest concept, commonly seen in aptitude tests to assess algebraic setup skills.

Given Data / Assumptions:

Total amount = Rs 1,500.
Let the amount at 6% per annum be x rupees.
Then the amount at 5% per annum is (1500 - x) rupees.
Total annual simple interest from both parts = Rs 85.
Simple interest for one year = (Principal * Rate * 1) / 100.

Concept / Approach:
We express the yearly interest from each part in terms of x, sum them, and equate to the given total of Rs 85. This gives a linear equation in a single variable x. Solving the equation yields the amount invested at 6%. Subtracting that from 1500 gives the amount invested at 5%, which is what the question asks.

Step-by-Step Solution:
Step 1: Let amount at 6% per annum be x. Step 2: Then amount at 5% per annum is 1500 - x. Step 3: Yearly simple interest from the 6% part: I_6 = (x * 6 * 1) / 100 = 0.06x. Step 4: Yearly simple interest from the 5% part: I_5 = ((1500 - x) * 5 * 1) / 100 = 0.05(1500 - x). Step 5: Total yearly interest is I_6 + I_5 = 85. Step 6: Form the equation: 0.06x + 0.05(1500 - x) = 85. Step 7: Expand and simplify: 0.06x + 75 - 0.05x = 85. Step 8: Combine like terms: (0.06x - 0.05x) + 75 = 85 gives 0.01x + 75 = 85. Step 9: Subtract 75 from both sides: 0.01x = 10. Step 10: Therefore, x = 10 / 0.01 = 1000. Step 11: Amount at 6% is Rs 1,000, so amount at 5% is 1500 - 1000 = 500.

Verification / Alternative check:
Check yearly interest with these values. At 6%, interest on Rs 1000 = 1000 * 6 / 100 = 60. At 5%, interest on Rs 500 = 500 * 5 / 100 = 25. Total yearly interest = 60 + 25 = 85, matching the given value. This confirms the amounts are correct.

Why Other Options Are Wrong:
If the amount at 5% were Rs 245, 635, 750, or 1250, the remaining amount at 6% would lead to a total interest different from Rs 85. These alternatives arise from incorrect setup or algebraic manipulation of the equation and therefore do not satisfy the condition given.

Common Pitfalls:
A typical error is to mix up which part is invested at which rate or to forget that the time period is one year. Another frequent problem is miscalculating the coefficients when collecting like terms. Carefully defining the variable and writing out the contributions to interest from each part helps reduce such mistakes.

Final Answer:
The amount invested at 5% per annum is Rs 500.