In how many years will ₹200 produce the same amount of simple interest at 5% per annum as ₹900 produces in 2 years at 3.5% per annum (simple interest in both cases)?

Introduction:
This question tests equating two simple interest amounts from different principals, rates, and times. The core idea is that simple interest is SI = (P * r * t)/100. If two investments produce the same simple interest, we can set their SI expressions equal and solve for the unknown time. Because it involves setting up an equation and solving for time, it is medium difficulty.

Given Data / Assumptions:

• Case 1 (unknown time): P1 = ₹200, r1 = 5% per annum, time = t years
• Case 2: P2 = ₹900, r2 = 3.5% per annum, time = 2 years
• Both are under simple interest
• Formula: SI = (P * r * t) / 100

Concept / Approach:
Compute SI from case 2 first since all values are known. Then set SI(case 1) equal to that value and solve for t. Keep percentages consistent and remember to divide by 100 only once in each SI formula.

Step-by-Step Solution:
SI2 = (900 * 3.5 * 2) / 100 SI2 = (900 * 7) / 100 = 6300 / 100 = 63 Now set SI1 = SI2: (200 * 5 * t) / 100 = 63 (1000 * t) / 100 = 63 10t = 63 t = 63 / 10 = 6.3

Verification / Alternative check:
At 5% on ₹200, yearly interest is ₹10. To reach ₹63, time must be 63/10 = 6.3 years, confirming the equation result.

Why Other Options Are Wrong:
5.2 years gives only ₹52 interest. 7 years gives ₹70 interest. 7.9 years gives ₹79 interest. 4.5 years gives ₹45 interest. Only 6.3 years yields ₹63.

Common Pitfalls:
Using 3.5% as 35%, forgetting to multiply by 2 years in case 2, or mixing up principal amounts between the two cases.

Final Answer:
It will take 6.3 years.