Simple Interest — Recover principal from given interest and partial year: What principal will earn a simple interest of Rs 55 in 9 months at a rate of 3 2/3% per annum?
Aptitude
Simple Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: 2000
Explanation
Introduction / Context:When the interest, time (including partial years), and rate are known under simple interest (SI), the principal can be obtained directly by inverting SI = P * r * t. Here the time is 9 months and the rate is 3 2/3% per annum.
Given Data / Assumptions:
- Simple interest SI = Rs 55
- Rate r = 3 2/3% per annum = 11/3 % = 11/300 as a decimal
- Time t = 9 months = 3/4 year
Concept / Approach:For simple interest: SI = P * r * t, where r is per year and t is in years. Rearranging gives P = SI / (r * t). The only care points are converting the mixed percentage to a decimal and months to a fraction of a year.
Step-by-Step Solution:
Convert rate: 3 2/3% = 11/3% = (11/3)/100 = 11/300 per year.Convert time: 9 months = 9/12 = 3/4 year.Compute principal: P = 55 / ((11/300) * (3/4)) = 55 / (11/400) = 55 * 400 / 11 = 2000.Verification / Alternative check:
Check SI with P = 2000: SI = 2000 * (11/300) * (3/4) = 2000 * 11 / 400 = 55 (matches).Why Other Options Are Wrong:
- 1000, 1500, 1800, 2500: Substituting these into SI = P * r * t does not yield Rs 55 for the given r and t.
Common Pitfalls:
- Using 9 as years instead of months; always convert months to year fraction.
- Mistaking 3 2/3% as 3.23% instead of 3.666...%.
Final Answer:Principal = Rs 2000.