Question : Rohan borrowed a certain sum of money at simple interest. The rate of interest was 3% per annum for the first 3 years, 4% per annum for the next 5 years and 6% per annum for the next 7 years. If he paid Rs. 2,059 as interest, then what is the sum borrowed (in Rs.)?
Option 1: 2400
Option 2: 2500
Option 3: 2900
Option 4: 3100
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Correct Answer: 2900
Solution :
Let the sum borrowed be $p$.
We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
So for the first 3 years at a 3% rate per annum, the interest of $p$ rupees is = $\frac{p×3×3}{100}$ = $\frac{9p}{100}$
For the next 5 years at a 4% rate per annum, the interest of $p$ rupees is = $\frac{p×4×5}{100}$ = $\frac{20p}{100}$
and for the next 7 years at a 6% rate per annum, the interest of $p$ rupees is = $\frac{p×6×7}{100}$ = $\frac{42p}{100}$
So, $(\frac{9p}{100} +\frac{20p}{100} +\frac{42p}{100}) = 2059$
⇒ $(9p+20p+42p) = 205900$
⇒ $71p = 205900$
$\therefore p=2900$
Hence, the correct answer is 2900.
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