On a certain sum of money, compounded annually, the difference between simple interest and compound interest for 2 years at an annual rate of 10% is Rs. 84. What is that sum of money?

1. A

   7,800 रूपये

2. B

   8,800 रूपये

3. C

   8,000 रूपये

4. D

   8,400 रूपये

Appeared in: CGHS SSC - 2018

Explanation

• The problem requires finding the principal amount (P) given the difference between compound interest (CI) and simple interest (SI) for 2 years at a specific rate.
• The standard shortcut formula for the difference between CI and SI for 2 years is: Difference = P × (Rate/100)2, which is derived from the basic formulas for SI and CI.
• Given the difference is Rs. 84 and the rate is 10%, we substitute these values into the formula: 84 = P × (10/100)2.
• Simplifying the equation gives 84 = P × (1/10)2 = P × (1/100).
• Solving for the Principal (P) by multiplying 84 by 100 results in P = Rs. 8,400.

Why Other Options Were Wrong

• Option A: This is an incorrect calculation. If the principal were Rs. 7,800, the difference between CI and SI for 2 years at 10% would be 7800 × (10/100)2 = 7800 × 0.01 = Rs. 78, not Rs. 84.
• Option B: This is an incorrect calculation. If the principal were Rs. 8,800, the difference between CI and SI for 2 years at 10% would be 8800 × (10/100)2 = 8800 × 0.01 = Rs. 88, not Rs. 84.
• Option C: This is an incorrect calculation. If the principal were Rs. 8,000, the difference between CI and SI for 2 years at 10% would be 8000 × (10/100)2 = 8000 × 0.01 = Rs. 80, not Rs. 84.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the principal amount based on the difference between compound and simple interest for a 2-year period as background academic context rather than a clinical decision trigger.
• This type of quantitative aptitude question is frequently included in the General Intelligence and Reasoning sections of nursing recruitment and other competitive examinations.
• Mastering basic financial mathematics, including simple and compound interest, is a key skill for scoring well in these sections.
• Knowing shortcut formulas, like the one for the 2-year difference between CI and SI, is crucial for saving time and improving accuracy during exams.

How to Approach the Question

• First, carefully read the question to identify the given parameters: the difference between CI and SI (Rs. 84), the time period (2 years), and the annual interest rate (10%).
• Recognize that the question asks for the principal sum and involves the difference between CI and SI over 2 years. This points towards a specific shortcut formula.
• Recall the formula: Difference = Principal × (Rate/100)2. This is much faster than calculating CI and SI separately.
• Substitute the known values into the formula: 84 = P × (10/100)2.
• Perform the arithmetic step-by-step to solve for the unknown variable, P.
• Simplify the equation: 84 = P × (1/10)2 = P × (1/100).

Concept Tested & Keywords

• Concept Tested: Calculating the principal amount based on the difference between compound and simple interest for a 2-year period.
• Stem keywords: sum of money, compounded annually, difference, simple interest, compound interest, 2 years, 10% annual rate
• Lead-in keywords: What is that sum of money?

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Q8_STYVQRFTBqb8dhfEokN

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