What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?

Appeared in: NCL (MP) Nursing Officer - 2019

Explanation

The formula for Simple Interest (SI) is SI = (P × R × T) / 100.
In this problem, the principal (P) and the rate of interest (R) are constant for both scenarios.
Therefore, the simple interest is directly proportional to the time (T).
The ratio of the simple interests will be equal to the ratio of the time periods.
Ratio = Time₁ : Time₂ = 6 : 9.
Simplifying the ratio 6:9 by dividing both numbers by their greatest common divisor (3) gives 2:3.

Option A: This ratio represents 1/3. The ratio of the given time periods is 6/9, which simplifies to 2/3, not 1/3.
Option B: This ratio represents 1/4. The ratio of the given time periods is 6/9, which simplifies to 2/3, not 1/4.
Option D: The data is adequate. Because the principal and rate are constant, their specific values are not required as they cancel out when forming the ratio.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Ratio of Simple Interest over different time periods as background academic context rather than a clinical decision trigger.
This question tests basic quantitative aptitude and logical reasoning, skills that are essential for problem-solving in various professional fields.
While not a direct clinical skill, proficiency in mathematics is necessary for nurses for tasks like medication dosage calculations, interpreting medical data, and managing fluid balances, where accuracy is critical for patient safety.
What if? If the question asked for the ratio of amounts after 6 and 9 years (using compound interest), the calculation would be much more complex and the data would likely be inadequate without the rate, as the principal would not simply cancel out.

How to Approach the Question

First, identify the core concept being tested, which is Simple Interest and ratios.
Recall the formula for Simple Interest: SI = (P × R × T) / 100.
Recognize the key information in the stem: the principal ('certain amount') and the 'same rate of interest' are constant.
Set up a ratio for the two scenarios: SI₁ (for 6 years) and SI₂ (for 9 years).
Notice that the constant terms (P, R, 100) will cancel out, simplifying the problem significantly.
The ratio of interests becomes the ratio of the time periods: 6 / 9.

Concept Tested & Keywords

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