Introduction
Successive borrowing/lending problems involve borrowing money at one rate and lending or re-borrowing it at another rate for overlapping time periods. These problems test how well you can track principal, rate, and exact time periods for each transaction.
Pattern: Successive Borrowing / Lending
Pattern
Key concept: Treat each transaction separately using the simple interest formula and then add or subtract the interest amounts to find the net result.
Formula:
SI = (P × R × T) / 100
where P = principal, R = rate (%), and T = time (years).
Step-by-Step Example
Question
Ramesh borrows ₹12,000 at 10% p.a. simple interest for 1 year. After 3 months, he lends ₹5,000 to Suresh at 14% p.a. for 9 months. Find the net interest Ramesh pays at the end of the year.
Options:
- A: ₹650
- B: ₹675
- C: ₹700
- D: ₹725
Solution
-
Step 1: Calculate SI on the amount borrowed
Borrowed: ₹12,000 at 10% for 1 year → SIpaid = (12000 × 10 × 1) / 100 = ₹1200. -
Step 2: Calculate SI on the amount lent to the other party
Lent: ₹5,000 at 14% for 9 months → 9 months = 9/12 = 0.75 year → SIreceived = (5000 × 14 × 0.75) / 100 = ₹525. -
Step 3: Compute net interest (paid - received)
Net interest = 1200 - 525 = ₹675. -
Final Answer:
₹675 → Option B -
Quick Check:
Interest paid = 1200, interest received = 525, difference = 675 ✅
Quick Variations
1. Lending or borrowing in multiple parts at different times.
2. Different durations for borrow and lend.
3. Questions may ask for net gain or loss percentage.
4. Time may be in months or days, convert to years correctly.
Trick to Always Use
- Step 1 → Break the timeline into blocks for each transaction.
- Step 2 → Apply SI formula separately for each block.
- Step 3 → Add/subtract interests to find the net result.
Summary
Summary
- Calculate SI separately for each borrowing or lending transaction.
- Convert all months or days into years correctly.
- Combine interest paid and interest received to get the net result.
- Use block-wise SI computation to avoid timing mistakes.
Example to remember:
Borrow ₹12,000 at 10% → Lend ₹5,000 at 14% → Net interest paid = ₹675.
Hint: Net interest = SI on borrowed - SI on lent.
Common Mistakes: Forgetting to subtract interest received.