The simple interest on a sum of money is equal to 4/9 of the principal. If the rate of interest and the time are numerically equal, the profit will be

Appeared in: ESIC Nursing Officer -2019 (Shift -1)

Explanation

The problem states that Simple Interest (SI) is 4/9 of the Principal (P), and the Rate (R) is equal to the Time (T).
Using the formula SI = (P × R × T) / 100, we can substitute the given values.
Replacing SI with (4/9)P and T with R gives the equation: (4/9)P = (P × R × R) / 100.
After canceling P from both sides, we get R² = 400/9.
Taking the square root gives R = 20/3, which is equal to the mixed fraction 6 2/3.

Option A: This is an incorrect calculation. If the rate were 6%, then R² would be 36. However, the calculation yields R² = 400/9, which is approximately 44.44.
Option B: This is an incorrect calculation. If the rate were 7%, then R² would be 49. The correct value for R² is 400/9 (approx 44.44).
Option C: This is a duplicate of option A and is incorrect for the same reason. A rate of 6% would mean R² is 36, which does not match the calculated R² of 400/9.

Visual 1: No visual is required for this type of quantitative aptitude question.

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.
While this is a non-nursing question, the analytical and problem-solving skills required are essential for nurses.
Nurses frequently perform calculations for drug dosages, IV drip rates, and other clinical parameters, which requires accuracy and a systematic approach similar to solving this problem.
What if the simple interest was 1/4 of the principal? In that case, R² would be 100/4 = 25, and the rate (R) would be 5%.

How to Approach the Question

First, carefully read the problem to identify all the given information and what needs to be found. Here, SI = (4/9)P and R = T.
Identify the relevant formula, which is the formula for simple interest: SI = (P × R × T) / 100.
Substitute the known values from the problem into the formula.
Simplify the equation by performing algebraic operations. In this case, cancel the 'P' term from both sides.
Solve the simplified equation for the unknown variable, which is 'R' (Rate).
Convert the final answer into the format required by the options (e.g., from an improper fraction to a mixed number).

Concept Tested & Keywords

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Practise the full ESIC Nursing Officer -2019 (Shift -1)

Attempt every question from this paper in a timed mock, then review the full solution for each one.