The simple interest on Rs. 2000 for 2 years is calculated at a rate described as Rs. 75 per thousand rupees per annum. When this rate is applied, what is the total simple interest earned in rupees over the 2-year period?

Introduction / Context:
This question is a basic test of interpreting a slightly unusual way of expressing the interest rate. Instead of giving a direct percentage, the lender states the rate as Rs. 75 per thousand rupees per annum. We must convert this description into a percentage rate and then apply the simple interest formula to find the total interest for 2 years on Rs. 2000.

Given Data / Assumptions:

• Principal P = Rs. 2000.
• Time T = 2 years.
• Rate is Rs. 75 interest per Rs. 1000 per year.
• Simple interest formula: SI = (P * R * T) / 100.

Concept / Approach:
If Rs. 75 is charged as interest on Rs. 1000 for 1 year, then the percentage rate per annum is (75 / 1000) * 100% = 7.5% per year. Once we have the percentage rate, we can plug it into the simple interest formula along with the principal and time to get the total interest.

Step-by-Step Solution:
Convert the rate: R = (75 / 1000) * 100 = 7.5% per annum. Principal P = 2000, time T = 2 years. Use SI formula: SI = (P * R * T) / 100. SI = (2000 * 7.5 * 2) / 100. First compute 2000 * 7.5 = 15000. Then SI = (15000 * 2) / 100 = 30000 / 100 = Rs. 300.
Verification / Alternative check:
Another way: If Rs. 1000 earns Rs. 75 per year, then Rs. 2000 (twice as much) earns Rs. 150 per year. Over 2 years, total interest = 2 * 150 = Rs. 300, matching our earlier calculation.

Why Other Options Are Wrong:
Rs. 150 corresponds to only one year of interest on Rs. 2000 at this rate, not 2 years. Rs. 400, Rs. 450, and Rs. 600 are larger than the correct value and arise from mistakenly treating the rate as 10%, 12%, or double-counting the time or principal.

Common Pitfalls:
A typical error is to misread “Rs. 75 per thousand per annum” as a flat amount regardless of principal size, or to forget to convert it into a percentage. Others forget to multiply by the full 2-year period or incorrectly divide by 100 more than once. Keeping track of units and conversion steps avoids these issues.

Final Answer:
The total simple interest earned in 2 years is Rs. 300.