Question : B borrows Rs. 5000 from A at 6% p.a. simple interest and lends it to C at compound interest of 10% p.a. If B collects the money back from C after 2 years and repays A, the profit made by B in the transaction is ______.
Option 1: Rs. 1050
Option 2: Rs. 500
Option 3: Rs. 450
Option 4: Rs. 600
Correct Answer: Rs. 450
Solution :
At Simple Interest, B borrows from A.
Principal = Rs. 5000
Rate = 6%
Time = 2 years
At Compound Interest, B lends to C.
Principal, $P$ = Rs. 5000
Time, $n$ = 2 years
Rate, $R$ = 10%
We know,
Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
Total amount = $P(1+\frac{R}{100})^{n}$
Simple interest = $\frac{5000 \times 2 \times 6}{100}$ = Rs. 600
Total amount to be paid back to A = 5000 + 600 = Rs. 5600
B lends to C at Compound interest.
Total amount = $5000(1+\frac{10}{100})^{2}$ = 5000 × 1.21= Rs. 6050
So, the profit made by B = Rs. 6050 – Rs. 5600 = Rs. 450
Hence, the correct answer is Rs. 450.
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