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 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 the original ₹30,000 did Aman borrow at 9 % p.a. from Lender A?
- (a)₹10,000
- (b)₹8,000
- (c)₹7,000
- (d)₹20,000
Answer
Why
Correct — D. Let x be the amount at 9%, so 30,000 − x is at 6%.
Interest at 9% for 4 years: 0.36x
Interest at 6% for 4 years: 0.24(30,000 − x) = 7,200 − 0.24x
Total: 0.12x + 7,200 = 9,600
Subtract 7,200: 0.12x = 2,400
Divide by 0.12: x = ₹20,000 → option (d)
Check the swap: ₹20,000 at 6% and ₹10,000 at 9% for 4 years
= 4,800 + 3,600 = ₹8,400, exactly ₹1,200 less than ₹9,600
Why the others are wrong
- (a)₹10,000 — ₹10,000 is the loan at 6% from Lender B. Putting ₹10,000 at 9% instead gives 3,600 + 4,800 = ₹8,400, the swapped figure, not the ₹9,600 paid.
- (b)₹8,000 — ₹8,000 at 9% and ₹22,000 at 6% earn 4 × (720 + 1,320) = ₹8,160 in four years, well short of ₹9,600.
- (c)₹7,000 — ₹7,000 at 9% and ₹23,000 at 6% earn 4 × (630 + 1,380) = ₹8,040. Moving money to the 9% lender raises the interest, so the answer lies higher.
Concept
Split-sum simple interest: call one part x and the other total − x, then set the combined interest equal to the figure given. The equation is linear, so one condition fixes x.
The swap is a second route. Swapping two principals changes the interest by time × rate gap × principal gap: 4 × 3% × gap = 1,200, so the gap is ₹10,000 and the loans are ₹20,000 and ₹10,000.
Because the actual interest was the higher figure, more money sat at the higher rate, so the ₹20,000 is the 9% loan. Both conditions agree on it.
The stem prints 'discovered that he interchanged the principal amounts taken from the two lenders, his four-year interest outgo would have been ₹1,200 less' without an 'if'. Read it as a what-if: ₹9,600 is what he actually paid.
Key facts
- Simple interest = principal × rate × time ÷ 100.
- Swapping two principals between two rates changes the interest by time × rate gap × principal gap.
- ₹20,000 at 9% and ₹10,000 at 6% for 4 years earn ₹7,200 + ₹2,400 = ₹9,600.
Study next
Common traps
- Leaving out the 4 years: 0.09x + 0.06(30,000 − x) = 9,600 gives x = ₹2,60,000, more than the whole loan.
- Answering with Lender B's ₹10,000 when the question asks for the 9% loan from Lender A.
The one-unknown split is asked at 10 Sep 2024, 09:00, Quant Q.2 (₹4,000 at 8% and 10% earning ₹352, so ₹1,600 at 10%) and at 17 Sep 2025, 16:00, Quant Q.7 (₹5000 at 6% and 9% earning ₹390, so ₹2000 at 6%).
An interchange supplies the second equation at 23 Sep 2024, 09:00, Quant Q.9, where swapping the counts of ₹20 and ₹10 notes cuts ₹390 by ₹90.
Related PYQs
No directly related past PYQ was found.