A sum of ₹4,000 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest (both per annum). If the total interest earned in 1 year from both parts together is ₹352, what is the amount (in rupees) lent at 8% per annum?

Introduction:
This question tests splitting a total principal into two parts with different simple interest rates such that the combined yearly interest is known. Because the time is 1 year, interest from each part is simply rate% of that part. This becomes a simple linear equation in the unknown split amount. The numbers are designed so the equation solves cleanly.

Given Data / Assumptions:

• Total principal = ₹4,000
• Part 1 at 8% per annum for 1 year
• Part 2 at 10% per annum for 1 year
• Total interest in 1 year = ₹352
• Formula for 1 year: SI = (P * r) / 100

Concept / Approach:
Let x be the amount lent at 8%. Then (4000 - x) is lent at 10%. Compute interest from each part for 1 year, add them, and set equal to 352. Solve for x.

Step-by-Step Solution:
Let x = amount at 8% Amount at 10% = 4000 - x Interest from 8% part (1 year) = (x * 8) / 100 = 0.08x Interest from 10% part (1 year) = ((4000 - x) * 10) / 100 = 0.10(4000 - x) Total interest: 0.08x + 0.10(4000 - x) = 352 0.08x + 400 - 0.10x = 352 -0.02x = -48 x = 2400

Verification / Alternative check:
If x=2400, interest at 8% is 192. Remaining 1600 at 10% gives 160. Total interest = 192+160 = 352, matching exactly.

Why Other Options Are Wrong:
Each incorrect split changes the weighted interest mix. For example, higher x reduces the 10% portion too much and total interest falls below 352, while lower x increases 10% portion too much and total interest exceeds 352.

Common Pitfalls:
Forgetting time is 1 year (so no need for t), mixing up which part is at 8% vs 10%, or adding rates directly instead of using a weighted sum.

Final Answer:
The amount lent at 8% per annum is ₹2,400.