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?

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:

Verification / Alternative check:

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.