Question

A man invested \(x\) rupees for \(y\) years at a rate of 3.25% per annum simple interest. If he received 3.25\(x\) after \(y\) years, find the value of \(y\).

• A. \(68.22 \)
• B. \(67.32 \)
• C. \(65.33 \)
• D. \(69.23 \)

Hint:

Always distinguish between "Interest received" and "Amount received." Amount = Principal + Interest.

Answer 1

The Correct Option is C

Concept: Simple Interest (S.I.) is calculated using the formula: \[ S.I. = \frac{P \times R \times T}{100} \] Where \(P\) is Principal, \(R\) is Rate of interest per annum, and \(T\) is Time in years.
Step 1: Identify the components from the question.
Principal (\(P\)) = \(x\)
Rate (\(R\)) = 3.25%
Time (\(T\)) = \(y\)
Simple Interest (\(S.I.\)) received = 3.25\(x\)

Step 2: Substitute values into the formula and solve for \(y\).
\[ 3.25x = \frac{x \times 3.25 \times y}{100} \] Divide both sides by \(3.25x\): \[ 1 = \frac{y}{100} \quad \Rightarrow \quad y = 100 \] Note: Based on the provided options, there is a discrepancy in the question's value or options. However, if the Interest received was \(x\) (making total amount \(3.25x\)), the math would align differently. Given the literal text, \(y = 100\). If we assume a typo in the problem and 3.25x is the Amount, then S.I = 2.25x. Let's re-calculate: \(2.25x = (x \cdot 3.25 \cdot y)/100 \Rightarrow y = 225/3.25 \approx 69.23\).