Simple Interest – Split a principal into two parts with equal interest earned: A sum of ₹ 1,521 is split into two parts. On one part, the interest at 10% per annum for 5 years is equal to the interest on the other part at 8% per annum for 10 years. What are the two parts?

Introduction / Context:
Equal-interest conditions on two parts of a principal under simple interest create a balance equation between rate * time * amount on each part.

Given Data / Assumptions:

• Total principal S = ₹ 1521
• Part x at 10% for 5 years → interest = x * 0.10 * 5 = 0.5x
• Other part (1521 − x) at 8% for 10 years → interest = (1521 − x) * 0.08 * 10 = 0.8(1521 − x)

Concept / Approach:
Set the two interests equal and solve for x, then compute the complementary part.

Step-by-Step Solution:
0.5x = 0.8(1521 − x)0.5x = 1216.8 − 0.8x1.3x = 1216.8 → x = 936Other part = 1521 − 936 = 585

Verification / Alternative check:
Interest on ₹ 936 at 10% for 5 years = 0.5 * 936 = 468; interest on ₹ 585 at 8% for 10 years = 0.8 * 585 = 468 (matches).

Why Other Options Are Wrong:
They pair sums that do not total ₹ 1521 and/or do not balance the interest equality.

Common Pitfalls:
Treating rates or times as percentages of the total rather than factors on each part; arithmetic slips when distributing 0.8.

Final Answer:
₹ 936 and ₹ 585