Srinivasan invests two equal amounts in two different banks. One bank offers simple interest at 8% per annum and the other offers simple interest at 12% per annum. At the end of one year, the total interest earned from both banks together is Rs 1500. Using this information, find the amount invested in each bank.

Introduction / Context:
This question deals with equal investments placed at different simple interest rates. Srinivasan invests the same principal in two banks, one at 8% and the other at 12%, and is told the total interest from both at the end of a year. The student must use the simple interest formula and the fact that the two principals are equal to form an equation in a single variable. Problems like this are common in aptitude tests and help students become comfortable with modeling financial situations using algebra.

Given Data / Assumptions:

• Two investments with equal principal amounts.
• Rate in Bank 1 = 8% per annum simple interest.
• Rate in Bank 2 = 12% per annum simple interest.
• Time period T = 1 year for both investments.
• Total interest from both banks together after 1 year = Rs 1500.
• Interest is calculated using simple interest only.

Concept / Approach:
Let the amount invested in each bank be P rupees. For simple interest over 1 year, the interest from the first bank is (P * 8 * 1) / 100 and from the second bank is (P * 12 * 1) / 100. The sum of these two interests is given to be Rs 1500. Thus, we can write an equation involving P and solve it. This is essentially a linear equation in one variable where the total interest is the sum of the individual interests at different rates.

Step-by-Step Solution:
Let P be the amount invested in each bank. Bank 1: Rate = 8% per annum, time = 1 year. Simple interest from Bank 1: SI1 = (P * 8 * 1) / 100 = 0.08P. Bank 2: Rate = 12% per annum, time = 1 year. Simple interest from Bank 2: SI2 = (P * 12 * 1) / 100 = 0.12P. Total interest from both banks = SI1 + SI2 = 0.08P + 0.12P. So total interest = 0.20P. Given that total interest is Rs 1500, we have 0.20P = 1500. P = 1500 / 0.20. P = 7500. Therefore, the amount invested in each bank is Rs 7500.

Verification / Alternative check:
Check the interest values with P = 7500. From Bank 1 at 8% for 1 year, interest = (7500 * 8) / 100 = 600. From Bank 2 at 12% for 1 year, interest = (7500 * 12) / 100 = 900. Total interest = 600 + 900 = 1500, which matches the given total interest. Thus, the solution is verified as correct.

Why Other Options Are Wrong:
If P were Rs 5800, total interest at 8% and 12% would be 0.20 * 5800 = 1160, not 1500.
If P were Rs 15000, total interest would be 3000, which is double the required value.
If P were Rs 17000, or Rs 6000, similar calculations show total interest values different from 1500. Only P = Rs 7500 satisfies the equation 0.20P = 1500.

Common Pitfalls:
Common mistakes include assuming the total principal in both banks is 1500 or miscalculating the combined rate as an average rather than summing the interest. Some learners also forget that the time is 1 year and may mistakenly multiply by a different period. Writing the expressions for SI1 and SI2 clearly and then adding them helps avoid such confusion.

Final Answer:
The amount invested in each bank by Srinivasan is Rs 7,500.