In aptitude (Simple Interest), what principal amount (in ₹) will yield a total simple interest of ₹60 at a rate of 6% per annum in 5 years? (Assume simple interest throughout and use the standard formula SI = P * r * t / 100.)

Introduction / Context:
This aptitude question checks your understanding of basic simple interest calculations and how to rearrange the standard formula to find the missing principal amount. Such questions are common in banking exams, government job tests, and campus placement aptitude rounds, where you must quickly identify which quantity is unknown and solve for it using the relationship between principal, rate, time, and interest earned.

Given Data / Assumptions:

• Simple interest (SI) earned = ₹60.
• Rate of interest per annum r = 6% per year.
• Time period t = 5 years.
• Interest is simple, so it is calculated only on the original principal for the full period.
• We need to find the principal amount P in rupees.

Concept / Approach:
In simple interest problems, the fundamental relationship between principal, rate, time, and interest is: SI = (P * r * t) / 100 Here SI is the simple interest, P is the principal, r is the annual rate in percent, and t is the time in years. When SI, r, and t are given, we solve this formula for P by rearranging it. This tests your ability to manipulate formulas and substitute known values correctly without making calculation errors.

Step-by-Step Solution:
Step 1: Start from the simple interest formula: SI = (P * r * t) / 100. Step 2: Substitute SI = 60, r = 6, and t = 5 into the formula. Step 3: So 60 = (P * 6 * 5) / 100. Step 4: Multiply the rate and time: 6 * 5 = 30, so 60 = (30 * P) / 100. Step 5: Rearrange to solve for P: P = 60 * 100 / 30. Step 6: Simplify the fraction: 60 * 100 = 6000 and 6000 / 30 = 200. Step 7: Therefore, the principal amount P is ₹200.

Verification / Alternative check:
We can verify the answer by plugging P = ₹200 back into the simple interest formula. Compute SI again: SI = (200 * 6 * 5) / 100 SI = (200 * 30) / 100 SI = 6000 / 100 = 60 The recalculated simple interest is ₹60, which matches the given data. This confirms that the principal of ₹200 is consistent and correct.

Why Other Options Are Wrong:
Option ₹250: If P were ₹250, SI would be (250 * 6 * 5) / 100 = ₹75, which is greater than ₹60.
Option ₹150: This gives SI = (150 * 6 * 5) / 100 = ₹45, which is less than ₹60.
Option ₹175: This gives SI = (175 * 6 * 5) / 100 = ₹52.5, not equal to ₹60.
Option ₹300: This gives SI = (300 * 6 * 5) / 100 = ₹90, again not matching ₹60.

Common Pitfalls:
Students often forget to divide by 100 when using percentage rates or accidentally use 6 or 5 instead of the product 6 * 5 while rearranging the formula. Another frequent mistake is to misplace SI and P in the formula, trying to compute interest instead of the principal. Working step by step and writing the formula clearly before substituting values helps avoid such errors in exam conditions.

Final Answer:
Therefore, the required principal amount that yields a simple interest of ₹60 at 6% per annum in 5 years is ₹200.