In aptitude (Simple Interest), a sum earns a total simple interest of ₹1,200 at a rate of 7.5% per annum in 4 years. What is the original principal sum (in ₹) that was invested?

Introduction / Context:
This is a straightforward simple interest problem where the total interest, rate, and time are given, and you must find the principal. Questions like this appear frequently in aptitude tests because they check quick application of the standard formula without any complex reasoning. Mastering these basics is important for clearing the quantitative section efficiently.

Given Data / Assumptions:

• Total simple interest SI = ₹1,200.
• Annual simple interest rate r = 7.5% per annum.
• Time period t = 4 years.
• We must find the principal amount P in rupees.
• Interest is calculated using simple interest, not compound interest.

Concept / Approach:
The standard simple interest formula is: SI = (P * r * t) / 100 Here SI is the simple interest, P is the principal, r is the rate in percent per annum, and t is time in years. When SI, r, and t are known, we can rearrange to solve for P: P = (SI * 100) / (r * t) The main task is accurate substitution and careful handling of the decimal rate 7.5%.

Step-by-Step Solution:
Step 1: Write the formula SI = (P * r * t) / 100. Step 2: Substitute SI = 1,200, r = 7.5, and t = 4. Step 3: 1,200 = (P * 7.5 * 4) / 100. Step 4: Multiply rate and time: 7.5 * 4 = 30. Step 5: So 1,200 = (P * 30) / 100. Step 6: Rearrange for P: P = 1,200 * 100 / 30. Step 7: Compute 1,200 * 100 = 120,000. Step 8: Divide 120,000 by 30 to get P = 4,000. Step 9: Therefore, the required principal is ₹4,000.

Verification / Alternative check:
Check by recomputing SI from P = ₹4,000: SI = (4,000 * 7.5 * 4) / 100 SI = (4,000 * 30) / 100 SI = 120,000 / 100 = 1,200 The calculated simple interest matches the given value of ₹1,200, so the principal is correct.

Why Other Options Are Wrong:
₹6,000: This gives SI = (6,000 * 7.5 * 4) / 100 = 1,800, which is higher than ₹1,200.
₹7,500: This leads to even larger interest and does not match the required total.
₹8,000: This produces SI = 2,400, exactly double the given interest.
₹5,000: This gives SI = (5,000 * 7.5 * 4) / 100 = 1,500, which again is not equal to ₹1,200.

Common Pitfalls:
One common mistake is mishandling the decimal rate 7.5%; some students approximate it poorly or forget to multiply it correctly by time. Others try to directly guess the principal from the options without using the formula, which can waste time. Writing the formula first, simplifying r * t, and then performing clean arithmetic reduces errors. Avoid using shortcuts unless you are very confident with percentage mental math.

Final Answer:
The principal sum that earns ₹1,200 as simple interest at 7.5% per annum over 4 years is ₹4,000.