Simple Interest — Borrow at 9%, add own money, lend at 12%: A borrows ₹ 4800 at 9% p.a. SI for 3 years. He adds some of his own money and lends the total at 12% p.a. SI for the same 3 years. If his net gain is ₹ 720, how much did he add?
Aptitude
Simple Interest
Difficulty: Medium
Choose an option
Answer
Correct Answer: ₹ 800
Explanation
Introduction / Context:Net profit in a borrow-and-lend setup equals interest earned on the lent total minus interest paid on the borrowed amount. With equal terms and simple interest, it becomes a straightforward linear equation in the added amount.
Given Data / Assumptions:
- Borrowed principal = ₹ 4800 at 9% for 3 years
- Let added amount = m; lent principal = 4800 + m at 12% for 3 years
- Net gain over 3 years = ₹ 720
Concept / Approach:Profit = (4800 + m) * 0.12 * 3 − 4800 * 0.09 * 3. Set equal to 720 and solve for m.
Step-by-Step Solution:
Profit = (4800 + m)*0.36 − 4800*0.27 = 1728 + 0.36 m − 1296 = 432 + 0.36 m.432 + 0.36 m = 720 ⇒ 0.36 m = 288 ⇒ m = 800.Verification / Alternative check:
Interest received: (5600)*0.36 = 2016; paid: 1296; difference = 720 (matches).Why Other Options Are Wrong:
- 500, 640, 740, 900 do not balance the profit equation to 720.
Common Pitfalls:
- Mixing rates or durations; both are 3 years so factors are comparable.
Final Answer:₹ 800.