In how many years will Rs. 200 produce the same amount of simple interest at 5% per annum as Rs. 900 produces in 2 years at 3 1/2% per annum?

Introduction / Context:
This question compares two simple interest scenarios. You know the interest earned on Rs. 900 at 3 1/2% per annum for 2 years, and you are asked to find how long Rs. 200 must be invested at 5% per annum to earn the same interest.

Given Data / Assumptions:

• First principal P1 = Rs. 900.
• First rate R1 = 3 1/2% per annum = 3.5% per annum.
• First time T1 = 2 years.
• Second principal P2 = Rs. 200.
• Second rate R2 = 5% per annum.
• Second time T2 is unknown and must be found such that both interests are equal.

Concept / Approach:
First compute the simple interest earned on Rs. 900 at 3.5% for 2 years. Then set the simple interest on Rs. 200 at 5% for T2 years equal to that amount. This gives a linear equation in T2 that you can solve directly.

Step-by-Step Solution:
Step 1: Compute the interest on Rs. 900 at 3.5% for 2 years using SI1 = (P1 * R1 * T1) / 100. Step 2: SI1 = (900 * 3.5 * 2) / 100. Step 3: 3.5 * 2 = 7, so SI1 = (900 * 7) / 100 = 6300 / 100 = Rs. 63. Step 4: Let T2 be the required time in years for the second case, with SI2 = (P2 * R2 * T2) / 100. Step 5: Substitute P2 = 200 and R2 = 5: SI2 = (200 * 5 * T2) / 100. Step 6: Simplify: (200 * 5) / 100 = 10, so SI2 = 10 * T2. Step 7: Set SI2 equal to SI1: 10 * T2 = 63. Step 8: T2 = 63 / 10 = 6.3 years.

Verification / Alternative check:
Check by computing the interest on Rs. 200 for 6.3 years at 5%. SI = (200 * 5 * 6.3) / 100 = (200 * 31.5) / 100 = 6300 / 100 = Rs. 63, which matches the interest on Rs. 900 at 3.5% for 2 years. This confirms that 6.3 years is correct.

Why Other Options Are Wrong:
5.2 years, 7 years, and 7.9 years all lead to interest values either lower or higher than Rs. 63 when used in the second scenario, so they do not satisfy the equality requirement.

Common Pitfalls:
Some students misinterpret 3 1/2% as 3.2% or 3.12%, which is incorrect. Others forget to equate the two interests or misapply the formula by adding interests instead of matching them. Paying attention to the wording “produce the same interest” is crucial.

Final Answer:
Rs. 200 will need to be invested for 6.3 yrs at 5% per annum to earn the same interest as Rs. 900 earns under the given conditions.