Difficulty: Medium
Correct Answer: 50%
Explanation:
Introduction / Context:
This question focuses on simple interest, where the interest is calculated on the original principal throughout the entire period. The situation where an amount becomes a multiple of the principal is very common in aptitude tests and helps in quickly finding the rate of interest.
Given Data / Assumptions:
Concept / Approach:
Under simple interest, Amount = Principal + Interest. If the amount is five times the principal, then interest equals four times the principal. The simple interest formula is I = (P * R * T) / 100, where P is principal, R is rate per annum and T is time in years. Using the relationship between interest and principal, we can solve for R.
Step-by-Step Solution:
Let principal = P.Given that amount after 8 years is 5P.So interest I = amount - principal = 5P - P = 4P.Simple interest formula: I = (P * R * T) / 100.Substitute I = 4P, T = 8 years.4P = (P * R * 8) / 100.Cancel P from both sides: 4 = (R * 8) / 100.Thus R * 8 = 400 and R = 400 / 8 = 50 percent per annum.
Verification / Alternative check:
If P = Rs. 100, then at 50 percent simple interest, yearly interest is Rs. 50. Over 8 years, total interest = 8 * 50 = Rs. 400. Amount = 100 + 400 = 500, which is exactly 5 times the principal, confirming our calculation.
Why Other Options Are Wrong:
Rates like 30 percent, 40 percent or 55 percent do not yield an amount that is 5P in 8 years. For example, at 40 percent, total interest in 8 years would be 3.2P, not 4P, giving an amount of 4.2P instead of 5P.
Common Pitfalls:
Students sometimes confuse simple interest with compound interest or misinterpret "five times" as an interest of 5P rather than an amount of 5P. Keep clear that amount equals principal plus interest, so the extra portion beyond the principal is the interest.
Final Answer:
The required simple interest rate is 50 percent per annum.
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