Difficulty: Easy
Correct Answer: 4 years
Explanation:
Introduction / Context:
This is a straightforward numerical question on simple interest, where you are given the principal amount, the total interest earned, and the rate of interest. You are required to find the time in years for which the money was invested.
Given Data / Assumptions:
Concept / Approach:
The formula for simple interest is SI = (P * R * T) / 100. When SI, P, and R are known, you can rearrange the formula to solve for time as T = (SI * 100) / (P * R). Substituting the known values will yield the required time in years.
Step-by-Step Solution:
Step 1: Write the formula for simple interest: SI = (P * R * T) / 100.
Step 2: Rearrange to find T: T = (SI * 100) / (P * R).
Step 3: Substitute SI = 81, P = 450, and R = 4.5.
Step 4: Compute T = (81 * 100) / (450 * 4.5).
Step 5: Calculate the denominator: 450 * 4.5 = 2025.
Step 6: Compute the numerator: 81 * 100 = 8100.
Step 7: Now T = 8100 / 2025 = 4 years.
Verification / Alternative check:
You can verify the answer by plugging T = 4 years back into the simple interest formula. SI = (450 * 4.5 * 4) / 100. First calculate 450 * 4.5 = 2025. Then 2025 * 4 = 8100. Finally, 8100 / 100 = 81, which matches the given interest, confirming that 4 years is correct.
Why Other Options Are Wrong:
3.5 years would give less than Rs. 81 as interest at 4.5% on Rs. 450, so it is too short.
4.5 years would result in more than Rs. 81 as interest, meaning the time would be too long.
5 years would further increase the interest beyond Rs. 81, so it is clearly incorrect.
Common Pitfalls:
A common mistake is to mix up the formula or to forget to divide by 100 when dealing with percentages. Some students also incorrectly treat 4.5% as 4.5 in the numerator without proper positioning in the formula. Carefully substituting values and simplifying step by step avoids these errors.
Final Answer:
The required time for Rs. 450 to earn Rs. 81 at 4.5% per annum is 4 years.
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