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
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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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