A certain sum becomes 5 times at 10% simple interest per year. At what yearly rate of interest it will become 7 times in same time?

1. A

   12%

2. B

   15%

3. C

   20%

4. D

   30%

Appeared in: UPPSC 2017

Explanation

• The problem requires finding a new simple interest rate when the time period is constant.
• First, calculate the time (T). If a sum P becomes 5P, the interest is 4P. Using SI = (PRT)/100, we get 4P = (P10T)/100, which gives T = 40 years.
• Next, calculate the new rate (R₂). If the sum P becomes 7P, the interest is 6P. Using the same formula with T=40, we get 6P = (PR₂40)/100.
• Solving for R₂ gives (6 * 100) / 40 = 15.
• Therefore, the new rate of interest is 15%.

Why Other Options Were Wrong

• Option A: This is an incorrect calculation. It may arise from a miscalculation in the steps, such as incorrectly dividing or multiplying the values.
• Option C: This value might be obtained if one assumes a simple doubling of the interest multiple (from 4P to 6P, a 1.5x increase) and applies it incorrectly, or makes a calculation error. For example, if the rate was doubled because the interest increased.
• Option D: This is a significant overestimation and likely results from a major error in setting up the proportion or formula, for instance, incorrectly calculating the interest earned in the second scenario.

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Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Simple Interest Calculation as background academic context rather than a clinical decision trigger.
• This question tests numerical aptitude, a fundamental skill for nurses.
• Accurate calculation is crucial in nursing for tasks like medication dosage calculation, IV drip rate regulation, and interpreting patient data charts.
• A mistake in calculation can have serious consequences for patient safety.

How to Approach the Question

• First, identify the type of question. This is a quantitative aptitude problem involving simple interest.
• Break down the information given: Initial condition (sum becomes 5 times at 10% rate) and the question (find the rate for the sum to become 7 times in the same time).
• Let the principal be 'P'. Calculate the simple interest for the first condition (SI₁ = 5P - P = 4P).
• Use the simple interest formula (SI = PRT/100) to find the unknown variable, which is Time (T) in this case.
• Now, use the calculated time (T=40 years) for the second condition. Calculate the new simple interest (SI₂ = 7P - P = 6P).
• Apply the simple interest formula again with the new SI and the constant T to find the new Rate (R₂).

Concept Tested & Keywords

• Concept Tested: Simple Interest Calculation
• Stem keywords: simple interest, sum becomes 5 times, 10% per year, becomes 7 times, same time
• Lead-in keywords: At what yearly rate

Question ID

QZ-mhFm4agoZrHA7UTJIV_

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