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?

Difficulty: Easy

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 = R


Why 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).

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