In how many years, a sum will be thrice of it at the rate of 10% per annum simple interest?

Appeared in: RRB Staff Nurse Mumbai-2015

Explanation

The question states the sum will be 'thrice' of itself, which means the final amount is 3 times the principal (A = 3P).
The Simple Interest (SI) earned is the difference between the Amount and the Principal (SI = A - P), which calculates to 3P - P = 2P.
Using the formula T = (SI × 100) / (P × R), we substitute the values: T = (2P × 100) / (P × 10).
The 'P' cancels out, and the equation simplifies to T = 200 / 10, which equals 20 years.

Option A: This would be the answer if the interest required was 1.5 times the principal (SI = 1.5P), not twice the principal.
Option C: This is a common error where the final amount (3P) is mistaken for the interest earned. The interest is only 2P.
Option D: This result would come from incorrectly assuming the interest earned is 4 times the principal.

Visual 1: Infographic: A simple bar chart showing the breakdown of the final amount. One block for Principal (P) and two blocks for Interest (2P), totaling three blocks for the final Amount (3P).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating Time in Simple Interest Problems as background academic context rather than a clinical decision trigger.
While this is a mathematics question, quantitative aptitude is a component of many nursing entrance and recruitment exams.
Strong analytical and calculation skills are essential for nurses for tasks like medication dosage calculation, IV drip rate monitoring, and interpreting patient data.
What if the interest was compounded annually? The time taken would be less. Using the compound interest formula A = P(1 + r/n)^(nt), we would solve 3 = (1.10)^t, which gives t = log(3)/log(1.10) ≈ 11.53 years. Simple interest is always calculated on the original principal only.

How to Approach the Question

First, identify the type of question. This is a quantitative aptitude problem involving Simple Interest.
Carefully read the question to identify the given values: the final amount is 'thrice' the principal (A=3P) and the rate is 10%.
Determine what you need to calculate. The question asks for the time period (T).
Calculate the Simple Interest (SI) earned. Remember, SI = Amount - Principal. In this case, SI = 3P - P = 2P.
Recall the correct formula: SI = (P × R × T) / 100. Rearrange it to solve for T: T = (SI × 100) / (P × R).
Substitute the known values into the formula and solve. Ensure you don't confuse the final amount (3P) with the interest earned (2P).

Concept Tested & Keywords

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Practise the full RRB Staff Nurse Mumbai-2015

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