Aman needed ₹30,000 for a start-up and split the sum between two private lenders under simple-interest terms:
Lender A charge 9% p.a. (simple interest)
Lender B charge 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 he 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 theoriginal ₹30,000 did Aman borrow at 9% p.a. from Lender A?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. ₹20,000.
Let amount taken at 9% = x
Then amount at 6% = 30000 − x
Interest for 4 years:
At 9% → x × 0.09 × 4 = 0.36x
At 6% → (30000 − x) × 0.06 × 4 = 0.24(30000 − x)
Total interest = 9600
So,
⇒ 0.36x + 0.24(30000 − x) = 9600
⇒ 0.36x + 7200 − 0.24x = 9600
⇒ 0.12x + 7200 = 9600
⇒ 0.12x = 2400
⇒ x = 20000
So, Aman borrowed ₹20,000 at 9%