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 Ahmedabad-2015

Explanation

The problem asks for the time (T) it takes for a principal sum (P) to become 3 times its value (3P) at a simple interest rate (R) of 10%.
The total Simple Interest (SI) earned must be the final amount minus the initial principal: SI = 3P - P = 2P.
Using the simple interest formula SI = (P × R × T) / 100, we can set up the equation: 2P = (P × 10 × T) / 100.
Solving for T, we cancel P from both sides: 2 = (10 × T) / 100, which simplifies to 2 = T / 10.
Therefore, T = 2 × 10 = 20 years.

Option A: In 15 years, the interest earned would be (P × 10 × 15) / 100 = 1.5P. The total amount would be P + 1.5P = 2.5P, not 3P.
Option C: In 30 years, the interest earned would be (P × 10 × 30) / 100 = 3P. The total amount would be P + 3P = 4P, not 3P.
Option D: In 40 years, the interest earned would be (P × 10 × 40) / 100 = 4P. The total amount would be P + 4P = 5P, not 3P.

Visual 1: Infographic: A bar chart showing the principal (P) as one block, and the final amount (3P) as three blocks. The two extra blocks are labeled as 'Simple Interest (2P)'.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the time period for a given simple interest rate and principal multiplication as background academic context rather than a clinical decision trigger.
This is a general aptitude question, not a clinical one. Strong quantitative skills are essential for various competitive exams, including those for nursing positions, for tasks like data interpretation and management.
Understanding percentages and growth rates is a foundational skill for interpreting statistics, research data, and even for financial planning.
What if the interest was compounded annually? If the interest were compounded, the time taken would be shorter because interest would be earned on previously accrued interest. The formula would be A = P(1 + R/100)^T, and we would solve 3 = (1.10)^T, which requires logarithms (T ≈ 11.5 years).

How to Approach the Question

First, identify the key components of the problem: the principal (let's call it P), the final amount (3P), and the rate of interest (10%).
Determine what you need to calculate, which is the time period (T).
Recall the relationship: Final Amount = Principal + Simple Interest. Use this to find the total simple interest that needs to be earned (SI = 3P - P = 2P).
Use the standard formula for Simple Interest: SI = (P × R × T) / 100.
Substitute the known values into the formula: 2P = (P × 10 × T) / 100.
Solve the resulting algebraic equation for T to find the answer.

Concept Tested & Keywords

Concept Tested: Calculating the time period for a given simple interest rate and principal multiplication.
Stem keywords: simple interest, rate, per annum, thrice
Lead-in keywords: In how many years

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