At what rate (in percentage) per annum will ₹1,300 give ₹520 as simple interest in 5 years?

Question

Examoogle · Accepted Answer

The correct answer is Option D: 8%. Calculate the total simple interest as a percentage of the principal: $(520 \div 1300) 	imes 100 = 40\%$. Since this interest is earned over 5 years, divide by 5 to get the annual rate: $40\% \div 5 = 8\%$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Calculate the total simple interest as a percentage of the principal: $(520 \div 1300) 	imes 100 = 40\%$. Since this interest is earned over 5 years, divide by 5 to get the annual rate: $40\% \div 5 = 8\%$.

Formula Used: $$R = \frac{SI 	imes 100}{P 	imes T}$$

Given: Principal (P) = ₹1,300, Simple Interest (SI) = ₹520, Time (T) = 5 years

Steps: Identify the given values from the question: We are given the Principal amount $P = 	ext{₹}1,300$, the Simple Interest $SI = 	ext{₹}520$, and the Time period $T = 5 	ext{ years}$.. State the standard formula for Rate of Interest: The formula for calculating the rate of interest ($R$) per annum in simple interest is derived from $SI = \frac{P 	imes R 	imes T}{100}$. Rearranging for $R$ gives: $$R = \frac{SI 	imes 100}{P 	imes T}$$. Substitute the values into the formula: Substitute $SI = 520$, $P = 1300$, and $T = 5$ into the rate equation: $$R = \frac{520 	imes 100}{1300 	imes 5}$$. Perform the calculation: Simplify the numerator and the denominator: $$R = \frac{52000}{6500} = \frac{520}{65} = 8\%$$

Answer: D is correct because substituting the given values into the simple interest formula yields a rate of 8% per annum.

Exam Tip: Always verify simple interest problems by recalculating the interest using the derived rate to ensure $SI = \frac{P 	imes R 	imes T}{100}$ matches the given interest.

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