Simple Interest – Equalize two borrowers’ amounts due: Suresh borrows ₹ 800 at 6% per annum (simple interest) and Naresh borrows ₹ 600 at 10% per annum (simple interest). After how many years will the amounts due (principal + interest) be equal?

Introduction / Context:
For simple interest, the amount owed after t years is A = P * (1 + r * t). Setting two such linear expressions equal allows solving for t.

Given Data / Assumptions:

• Suresh: P1 = ₹ 800, r1 = 6% per annum
• Naresh: P2 = ₹ 600, r2 = 10% per annum
• Find t such that A1 = A2

Concept / Approach:
Equate A1 = 800(1 + 0.06 t) and A2 = 600(1 + 0.10 t), then solve for t.

Step-by-Step Solution:
800 + 48t = 600 + 60t200 = 12t → t = 200 / 12 = 16 2/3 years

Verification / Alternative check:
At t = 16 2/3, A1 = 800 + 48*(16 2/3) = 800 + 800 = 1600; A2 = 600 + 60*(16 2/3) = 600 + 1000 = 1600.

Why Other Options Are Wrong:
5 1/3, 14 1/2, and 18 1/3 years produce unequal amounts.

Common Pitfalls:
Equating interests instead of amounts; forgetting to multiply rate by principal.

Final Answer:
162/3 yr