Introduction / Context:
This is a standard reverse simple interest problem. Instead of asking for interest, we are given the principal, rate, and interest, and we must find the time period. Such questions test whether you can manipulate the simple interest formula to solve for different variables, not just the interest amount.
Given Data / Assumptions:
- Principal (P) = Rs. 450
- Rate (R) = 4.5% per annum
- Simple interest (SI) = Rs. 81
- We assume simple interest throughout, not compound interest
Concept / Approach:The formula for simple interest is:
SI = (P * R * T) / 100We are required to find the time T in years. Rearranging the formula to solve for T gives:
T = (SI * 100) / (P * R)We simply substitute the given values into this rearranged formula and compute the answer.
Step-by-Step Solution:Given SI = 81, P = 450, R = 4.5T = (81 * 100) / (450 * 4.5)First compute the denominator: 450 * 4.5 = 2025Now compute the numerator: 81 * 100 = 8100So T = 8100 / 2025Divide: 8100 / 2025 = 4Therefore, T = 4 yearsVerification / Alternative check:We can check the result by computing the interest for 4 years. For 4 years, simple interest would be:
SI = (450 * 4.5 * 4) / 100= 450 * 18 / 100= 8100 / 100 = Rs. 81This matches the given interest, confirming that the time period of 4 years is correct.
Why Other Options Are Wrong:For 2 years, the interest would be half of 81, that is Rs. 40.50. For 2.5 or 3.5 years, the interest would be in between, not exactly Rs. 81. Only at 4 years does the interest reach exactly Rs. 81, so other options are not correct.
Common Pitfalls:Students sometimes forget to multiply the rate by time or misplace the 100 in the formula when solving for time. Another frequent error is to approximate 4.5% incorrectly. Always work step by step, keeping track of numerator and denominator carefully.
Final Answer:The required time for the interest to reach Rs. 81 is
4 years.
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