Question : Rohan borrows a certain sum at simple interest. The rate of interest is 3 percent per annum for the first 3 years, 4 percent per annum for the next 5 years, and 6 percent per annum for the next 7 years. If he paid Rs. 2485 as interest, then what is the sum borrowed?
Option 1: Rs. 2500
Option 2: Rs. 3500
Option 3: Rs. 4000
Option 4: Rs. 3600
Correct Answer: Rs. 3500
Solution :
Use the formula below.
Simple interest = $\frac{\text{Principle×Rate×Time}}{100}$
Let's denote the principal amount (the sum borrowed) as P
Simple interest for the first 3 years at 3 percent per annum
= $\frac{3}{100}$ × P × 3
Simple interest for the next 5 years at 4 percent per annum
= $\frac{4}{100}$ × P × 5
Simple interest for the next 7 years at 6 percent per annum
= $\frac{6}{100}$ × P × 7
Total Interest = $\frac{3}{100}$ × P × 3 + $\frac{4}{100}$ × P × 5 + $\frac{6}{100}$ × P × 7
⇒ 2485 = $\frac{9P}{100}$ + $\frac{20P}{100}$ + $\frac{42P}{100}$ = $\frac{71P}{100}$
⇒ 248500 = 71P
⇒ P = $\frac{248500}{71}$ = 3500
Hence, the correct answer is Rs. 3500.
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