Simple Interest – Parameterized symbol problem: The simple interest at R percent per annum for R years is Rs R. On what principal will this occur?
Aptitude
Simple Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: Rs (100/R)
Explanation
Introduction / Context:This symbolic question checks formula manipulation in simple interest: SI = P * r * t, with r expressed in percent per annum and t in years.
Given Data / Assumptions:
- SI = R rupees
- Rate = R% per annum = R / 100 per annum
- Time = R years
Concept / Approach:Using SI = P * (R / 100) * R, solve for P such that SI equals R rupees.
Step-by-Step Solution:
SI = P * (R / 100) * R = P * (R^2 / 100)Set SI = R → P * (R^2 / 100) = RP = R * 100 / R^2 = 100 / RHence P = Rs (100 / R)Verification / Alternative check:
Substitute back: SI = (100 / R) * (R / 100) * R = RWhy Other Options Are Wrong:
- Rs R / Rs 100R / Rs (R/100): dimensionally incorrect.
- Rs (100/R2): miswritten as R squared in denominator without proper notation; intended value is 100 / R.
Common Pitfalls:
- Mishandling the percent-to-decimal conversion.
Final Answer:Rs (100/R).