Aman needed ₹30,000 for a start-up and split the sum between two private lenders under simple-interest terms: Lender A charges 9% p.a. (simple interest) Lender B charges 6% p.a. (simple interest) Aman kept both loans exactly 4 years and then made a single lump-sum payment that settled only the accumulated interest, which came to ₹9,600. After preparing his books of account, Aman discovered that if he had interchanged the principal amounts taken from the two lenders, his four-year interest outgo would have been ₹1,200 less than what he actually paid. How much of the original ₹30,000 did Aman borrow at 9% p.a. from Lender A?
₹20,000
Step 1 – set up. Let A's amount = ₹x and B's amount = ₹(30000 − x).
Step 2 – original 4-year interest = ₹9,600:
\(\dfrac{x \times 9 \times 4}{100} + \dfrac{(30000 - x) \times 6 \times 4}{100} = 9600\)
\(\dfrac{36x}{100} + \dfrac{24(30000 - x)}{100} = 9600\)
Multiply by 100: \(36x + 720000 - 24x = 960000\)
\(12x = 240000 \implies x = 20000\)
Step 3 – verify with the swap condition. If amounts are interchanged, A's ₹20,000 goes to B (6%) and B's ₹10,000 goes to A (9%):
New interest \(= \dfrac{10000 \times 9 \times 4}{100} + \dfrac{20000 \times 6 \times 4}{100} = 3600 + 4800 = 8400\)
Difference \(= 9600 - 8400 = 1200\) ✓
Hence, Aman borrowed ₹20,000 from Lender A at 9% p.a.
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Important Questions from Simple Interest
- How long will it take for ₹1,500 to become ₹2,040 at a rate of 8% per annum simple interest?
- Find the simple interest (in ₹) if a sum of ₹400 is borrowed for 5.5 years at 12% per annum rate of interest.
- Find the simple interest (in ₹) if a sum of ₹400 is borrowed for 4.5 years at 8% per annum rate of interest.
Find the simple interest (in ₹) if a sum of ₹400 is borrowed for 5.5 years at 4% per annum rate of interest.
- Find the simple interest (in ₹) on ₹1,200 at an interest rate of 3% per month for 11 months.
