Find the simple interest on Rs. 6,250 at 14% per annum for a period of 146 days, assuming a 365 day year.

Introduction / Context:
This question checks your understanding of simple interest when the time period is given in days rather than in full years. In competitive exams, it is common to convert days into years using a 365 day year before applying the simple interest formula. Correct handling of this conversion is essential to get the right answer.

Given Data / Assumptions:

• Principal (P) = Rs. 6,250
• Rate of interest (R) = 14% per annum
• Time (T) = 146 days
• Assume 1 year = 365 days

Concept / Approach:
Simple interest is calculated using the formula:
Simple interest = (P * R * T) / 100When time is given in days, we must first convert it into years by dividing the number of days by 365. This converted time in years is then substituted into the formula. No compounding is involved because the interest is simple, not compound.

Step-by-Step Solution:
Convert time into years: T = 146 / 365 yearsSimple interest = (6250 * 14 * 146) / (100 * 365)First, compute the denominator: 100 * 365 = 36500Now compute the numerator: 6250 * 14 * 146We can cancel terms: 6250 / 36500 = 1 / 5.84, but a simpler process is standard exam simplification.Using direct calculation, the value comes out to Rs. 350
Verification / Alternative check:
We can approximate to verify the reasonableness. One year interest at 14% on Rs. 6,250 is:
(6250 * 14) / 100 = Rs. 875Now 146 days is a little less than 5 months, which is about 4 months out of 12, or roughly 0.4 of a year. Multiplying 875 by about 0.4 gives approximately 350, which confirms that Rs. 350 is a sensible and accurate answer.

Why Other Options Are Wrong:
Rs. 450, Rs. 550 and Rs. 650 are all higher than the correct value and would correspond to either a longer time period or a higher rate of interest. They do not match the given data after converting days into years.

Common Pitfalls:
A very common mistake is to treat 146 as if it were years or months directly without converting days into years. Another error is to assume a 360 day year without being instructed to do so, leading to a slightly different interest value. Students must read the question carefully and apply the correct time conversion.

Final Answer:
The simple interest on Rs. 6,250 for 146 days at 14% per annum is Rs. 350.