Two-part lending at 8% and 10% — find the 8% portion: A sum of ₹ 4000 is lent out partly at 8% and partly at 10% simple interest. If the total annual interest is ₹ 352, how much was lent at 8%?

Introduction / Context:
Another weighted-average style SI problem: the total interest is the sum of interests from each part. A single linear equation in one variable solves the split between 8% and 10%.

Given Data / Assumptions:

• Total principal = ₹ 4000
• x at 8% p.a.; (4000 − x) at 10% p.a.
• Total annual SI = ₹ 352

Concept / Approach:
Form the equation 0.08x + 0.10(4000 − x) = 352 and solve for x.

Step-by-Step Solution:
0.08x + 0.10 * 4000 − 0.10x = 3520.08x + 400 − 0.10x = 352−0.02x = −48 → x = 2400

Verification / Alternative check:
Interest from ₹ 2400 at 8% = ₹ 192; from ₹ 1600 at 10% = ₹ 160; total = ₹ 352 (correct).

Why Other Options Are Wrong:
Other choices do not satisfy the total interest constraint simultaneously for 8% and 10%.

Common Pitfalls:
Sign errors while combining 0.08x and −0.10x; forgetting that total principal is fixed at ₹ 4000.

Final Answer:
₹ 2400