X took a loan of Rs. 4000 with simple interest for as many years as the rate of interest. If he paid Rs. 1210 as interest at the end of the period, what was the rate of interest?

1. A

   4.5%

2. B

   7.5%

3. C

   5.5%

4. D

   6.5%

Appeared in: NORCET 2 -2021 (Shift-2)

Explanation

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• The fundamental formula for simple interest is SI = (P × R × T) / 100.
• The problem states that the number of years (T) is equal to the rate of interest (R), so we can substitute T with R, making the equation SI = (P × R²) / 100.
• Substituting the given values: Principal (P) = 4000 and Simple Interest (SI) = 1210.
• The equation becomes 1210 = (4000 × R²) / 100, which simplifies to 1210 = 40 × R².
• Solving for R², we get R² = 1210 / 40 = 30.25.
• Taking the square root of 30.25 gives R = 5.5. Thus, the rate of interest is 5.5%.

Why Other Options Were Wrong

• Option A: This is an incorrect calculation. It may result from an error in dividing 1210 by 40 or in finding the square root of 30.25.
• Option B: This value is incorrect. A common mistake could be misplacing the decimal or an error in the square root calculation.
• Option D: This is an incorrect calculation. It might arise from incorrectly simplifying the equation, for example, R² = 1210 / 30, or from an error in calculating the square root.

Related Visual

• Visual 1: Infographic: A visual breakdown of the Simple Interest formula (SI = PxRxT/100) showing how to substitute T=R and solve for R step-by-step.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the rate of interest when the time period is equal to the rate as background academic context rather than a clinical decision trigger.
• This question tests quantitative aptitude, a skill essential for various competitive examinations, including those for nursing recruitment, to assess problem-solving and analytical abilities.
• While not a clinical question, understanding financial calculations can be useful for nurses in administrative roles or for personal financial planning.
• What if the interest was compounded annually? If the interest was compounded, the formula would be A = P(1 + R/100)^T, and the interest would be A - P. The calculation would be more complex, involving logarithms or iterative methods to solve for R when T=R.

How to Approach the Question

• First, carefully read the question to identify all the given data: Principal (P = 4000), Simple Interest (SI = 1210).
• Identify the key relationship described in the problem: the time period in years (T) is the same as the rate of interest (R). This means T = R.
• Recall the standard formula for Simple Interest: SI = (P × R × T) / 100.
• Substitute the condition T = R into the formula, which modifies it to SI = (P × R × R) / 100 or SI = (P × R²) / 100.
• Plug the given numerical values (P and SI) into this modified formula.
• Solve the resulting algebraic equation for R. This will involve isolating R² and then taking the square root to find R.

Concept Tested & Keywords

• Concept Tested: Calculating the rate of interest when the time period is equal to the rate.
• Stem keywords: loan, simple interest, rate of interest, years
• Lead-in keywords: what was

Question ID

Q4GwZm5afTJzvJffFY4V1T

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