Question : The rate of interest for the first 2 years is 6% p.a., for the next 3 years is 10% p.a., and for the period beyond 5 years is 12% p.a. If a person gets INR 12,771 as simple interest after 7 years, then how much money did he invest?
Option 1: INR 20,000
Option 2: INR 19,350
Option 3: INR 19,450
Option 4: INR 19,300
Correct Answer: INR 19,350
Solution :
Let the principal be $P$.
Here SI is simple interest, R is the rate and T is the time.
For the first 2 years
SI = $\frac{\text{(P × 6 × 2)}}{100}=\frac{3P}{25}$
For the next 3 years
SI = $\frac{\text{(P × 10 × 3)}}{100}=\frac{3P}{10}$
For the next 2 years
SI = $\frac{\text{(P × 12 × 2)}}{100}=\frac{6P}{25}$
Total Interest in 7 years = INR 12771
⇒ $\frac{3P}{25}+\frac{3P}{10}+\frac{6P}{25}=12771$
⇒ $\frac{33P}{50} = 12771$
$\therefore P = 19350$
Hence, the correct answer is INR 19350.
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