What sum (in ₹) will earn a simple interest of ₹480 in 3 years at 20% per year rate of interest?

Appeared in: JIPMER Nursing Officer-2024

Explanation

The question asks to find the principal amount (P) given the simple interest (SI), rate (R), and time (T).
The formula for simple interest is SI = (P × R × T) / 100.
To find the principal, the formula is rearranged to P = (SI × 100) / (R × T).
Substituting the given values: P = (480 × 100) / (20 × 3).
Calculation: P = 48000 / 60, which simplifies to P = 800.
Thus, the required sum is ₹800.

Option B: If the principal were ₹400, the simple interest would be (400 × 20 × 3) / 100 = ₹240, which is not the ₹480 given in the problem.
Option C: If the principal were ₹1600, the simple interest would be (1600 × 20 × 3) / 100 = ₹960. This is double the interest amount specified.
Option D: If the principal were ₹1200, the simple interest would be (1200 × 20 × 3) / 100 = ₹720, which is incorrect.

Visual 1: Infographic: A visual breakdown of the simple interest formula rearranged to solve for the Principal (P). It would show the equation P = (SI × 100) / (R × T) with placeholders for each value, then show the numbers from the question being substituted to arrive at the answer.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the Principal in Simple Interest as background academic context rather than a clinical decision trigger.
This question tests basic numeracy and problem-solving skills, which are foundational for various calculations in a professional setting, including non-clinical roles.
Understanding how to manipulate formulas is a key analytical skill applicable to many fields.
What if the interest was compounded annually? The calculation would be more complex, using the formula A = P(1 + R/n)^(nt), and we would need to solve for P differently, highlighting the importance of identifying the correct formula for a given problem.

How to Approach the Question

First, identify all the given values in the question: Simple Interest (SI = ₹480), Time (T = 3 years), and Rate (R = 20%).
Next, identify what you need to find: the Principal sum (P).
Recall the standard formula for Simple Interest: SI = (P × R × T) / 100.
Rearrange this formula algebraically to solve for the unknown variable, P. This gives you P = (SI × 100) / (R × T).
Substitute the known values into the rearranged formula and perform the calculation.
Verify your answer by calculating the SI with the found principal: (800 × 20 × 3) / 100 = ₹480. This matches the given SI, confirming the answer is correct.

Concept Tested & Keywords

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