Rs. 1500 is divided into two parts so that if one part is invested at 6% per annum and the other part is invested at 5% per annum, the total simple interest from both parts in one year is Rs. 85. How much money is invested at 5%?

Introduction / Context:
This is a simple interest and ratio type question. A fixed amount is split into two parts and invested at different interest rates, 6% and 5%, for the same period of one year. The total interest received from both parts is known. From this information, we must determine how much is invested at the lower rate of 5% per annum.

Given Data / Assumptions:

• Total principal amount is Rs. 1500.
• One part of the money is invested at 6% per annum.
• The remaining part is invested at 5% per annum.
• Total simple interest from both parts after one year is Rs. 85.
• Interest is simple interest, and the time period is one year for both investments.

Concept / Approach:
Let x be the amount invested at 5% per annum. Then the remaining amount, 1500 - x, is invested at 6% per annum. Simple interest for one year is given by Principal * Rate / 100. We can write an equation based on the sum of the interests from the two parts being equal to Rs. 85. Solving this linear equation in x gives the amount invested at 5%.

Step-by-Step Solution:
Step 1: Let x be the amount invested at 5% per annum. Step 2: Then the remaining amount invested at 6% is 1500 - x. Step 3: Interest from the amount at 5% for one year is (x * 5 / 100) = 0.05x. Step 4: Interest from the amount at 6% for one year is ((1500 - x) * 6 / 100) = 0.06(1500 - x). Step 5: Total interest is given as Rs. 85, so write the equation 0.05x + 0.06(1500 - x) = 85. Step 6: Expand the second term: 0.05x + 0.06 * 1500 - 0.06x = 85. Step 7: Compute 0.06 * 1500 = 90. So the equation becomes 0.05x + 90 - 0.06x = 85. Step 8: Combine like terms for x: (0.05x - 0.06x) + 90 = 85, which simplifies to -0.01x + 90 = 85. Step 9: Subtract 90 from both sides: -0.01x = -5. Step 10: Divide by -0.01 to get x = 500. Step 11: Therefore, Rs. 500 is invested at 5% per annum.

Verification / Alternative check:
If Rs. 500 is invested at 5%, the interest from this part is 500 * 5 / 100 = Rs. 25. The remaining amount is 1500 - 500 = Rs. 1000, invested at 6%, giving interest 1000 * 6 / 100 = Rs. 60. Total interest is 25 + 60 = Rs. 85, which matches the given total. This confirms that x = 500 is correct.

Why Other Options Are Wrong:
If Rs. 600 were invested at 5%, the interest from that part would be 600 * 5 / 100 = Rs. 30 and the other part would be 900 at 6%, giving 54. Total interest would be 84, not 85. Similarly, other values like Rs. 450, Rs. 550 or Rs. 400 do not produce a total interest of exactly Rs. 85 when substituted into the equation. Only Rs. 500 satisfies the condition.

Common Pitfalls:
Some learners mistakenly assign x to the 6% part or write the total as 6x + 5(1500 - x) instead of correctly adjusting the rates. Others forget to divide by 100 when converting percentages to decimal rates. Solving the equation carefully and checking by direct substitution at the end is a good way to avoid these errors.

Final Answer:
The amount invested at 5% per annum is Rs. 500, which is option A.