Question : A man borrowed a certain sum of money at the rate of 10% per annum simple interest for the first three years and 15% per annum simple interest for the period beyond three years. If he pays a total interest of INR 2,884.50 at the end of 7 years, then the sum of money (in INR) that he borrowed is:
Option 1: 3,860
Option 2: 3,090
Option 3: 4,550
Option 4: 3,205
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Correct Answer: 3,205
Solution :
Let the principal be Rs. $x$
Rate = 10% per annum
Time = 3 years
Simple interest $=\frac{\text{Principal × Rate × Time}}{100}=\frac{ x \times 10 \times 3}{100}=\frac{3x}{10}$
After 3 years,
Principal = Rs. $x$
Rate = 15% per annum
Time = 4 years
Simple interest = $\frac{ x \times 15 \times 4}{100}=\frac{6x}{10}$
Total simple interest = $\frac{3x}{10}+\frac{6x}{10}=\frac{9x}{10}$
According to the question,
$\frac{9x}{10} = 2884.50$
$\therefore x = 3205$
Hence, the correct answer is INR 3,205.
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