The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 19% per annum is ₹664. Find the sum. (Answer to be rounded off to the nearest integer.)

1. A

   ₹18,404

2. B

   ₹18,388

3. C

   ₹18,396

4. D

   ₹18,393

Appeared in: Bihar NHM CHO-2025

Explanation

• The difference between compound interest (CI) and simple interest (SI) for 2 years is calculated using the formula: Difference = P × (R/100)², where P is the principal and R is the rate.
• Given the difference is ₹664 and the rate is 19%, we can set up the equation: 664 = P × (19/100)².
• Solving for P involves rearranging the formula: P = Difference / (R/100)².
• Substituting the values: P = 664 / (0.19)² = 664 / 0.0361.
• The calculation yields P ≈ 18393.35, which when rounded to the nearest integer is ₹18,393.

Why Other Options Were Wrong

• Option A: This value is incorrect and would result from a miscalculation. For example, incorrectly calculating (19/100)² or an error in the final division.
• Option B: This is an incorrect calculation. It does not match the result obtained by correctly applying the formula.
• Option C: This value is close but incorrect. It might arise from premature rounding during intermediate steps or a slight calculation error.

Related Visual

• Visual 1: Infographic: A clear infographic showing the formulas for Simple Interest, Compound Interest, and the specific shortcut formulas for the difference between CI and SI for 2 and 3 years. This provides a quick visual reference for key formulas.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the principal sum based on the difference between compound and simple interest as background academic context rather than a clinical decision trigger.
• This type of quantitative aptitude question is common in the non-nursing sections of nursing recruitment exams, testing logical and mathematical reasoning.
• Mastery of these problems demonstrates an ability to understand and apply formulas, a skill useful in various detail-oriented tasks.
• What if the time period was 3 years? The formula would change to: Difference = P × (R/100)² × (3 + R/100). Using this different formula is critical for problems with a 3-year timeframe.

How to Approach the Question

• First, identify all the given information in the problem: the difference between CI and SI (₹664), the time period (2 years), and the annual interest rate (19%).
• Recognize that this is a direct application problem. Recall the specific shortcut formula for the difference between CI and SI for a 2-year period: Difference = P × (R/100)².
• Substitute the given values into the formula: 664 = P × (19/100)².
• Systematically solve the equation for the unknown variable, P (the principal sum).
• Perform the calculation: P = 664 / 0.0361.
• Finally, round the result to the nearest integer as instructed in the question and select the matching option.

Concept Tested & Keywords

• Concept Tested: Calculating the principal sum based on the difference between compound and simple interest.
• Stem keywords: simple interest, compound interest, difference, 2 years, 19% per annum, ₹664
• Lead-in keywords: Find the sum

Question ID

QijmA0MBt-Hi6O_0xr2Thx

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