The Simple interest on a certain sum at a rate of 5% per annum for 3 years and 4 years differs by Rs. 42. The sum is :

Appeared in: RRB Staff Nurse Delhi-2015

Explanation

The problem states that the difference in simple interest between 4 years and 3 years is Rs. 42.
This difference corresponds to the simple interest earned for exactly one year (4 - 3 = 1 year).
The formula for Simple Interest (SI) is SI = (Principal × Rate × Time) / 100.
Substituting the values for one year: 42 = (P × 5 × 1) / 100.
Solving for the Principal (P), we get P = (42 × 100) / 5.
This calculation results in P = 840.

Option A: If the principal were Rs. 210, the simple interest for one year at 5% would be (210 × 5 × 1) / 100 = Rs. 10.5, which is not the given difference of Rs. 42.
Option B: If the principal were Rs. 280, the simple interest for one year at 5% would be (280 × 5 × 1) / 100 = Rs. 14, which does not match the given difference of Rs. 42.
Option C: If the principal were Rs. 750, the simple interest for one year at 5% would be (750 × 5 × 1) / 100 = Rs. 37.5, which is not the given difference of Rs. 42.

Visual 1: Infographic: A visual breakdown of the Simple Interest formula (SI = PxRxT/100) with clear labels for each component: Principal, Rate, Time, and Interest.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the Principal Amount in Simple Interest as background academic context rather than a clinical decision trigger.
While not a direct clinical question, proficiency in basic mathematics is a critical competency for nurses.
This skill is essential for accurate medication dosage calculations, determining IV drip rates, and interpreting quantitative data from patient monitoring devices.
Errors in calculation can have serious patient safety consequences, making numeracy a foundational professional requirement.

How to Approach the Question

First, carefully read the question to identify the given variables: Rate (R = 5%), Time 1 (T1 = 3 years), Time 2 (T2 = 4 years), and the difference in Simple Interest (Rs. 42).
Recognize the core concept: In simple interest, the interest earned each year is constant. Therefore, the difference in interest between two time periods is simply the interest for the time difference.
Calculate the difference in time: 4 years – 3 years = 1 year.
Equate the given interest difference to the interest for this time period. So, the Simple Interest for 1 year is Rs. 42.
Use the standard Simple Interest formula: SI = (P × R × T) / 100.
Substitute the known values (SI = 42, R = 5, T = 1) into the formula and rearrange it to solve for the unknown Principal (P).

Concept Tested & Keywords

Concept Tested: Calculating the Principal Amount in Simple Interest
Stem keywords: Simple interest, sum, rate, 5%, 3 years, 4 years, differs by Rs. 42
Lead-in keywords: The sum is

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Practise the full RRB Staff Nurse Delhi-2015

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