Question : The simple interest on a sum for 5 years is Rs. 7,590. The rate of interest for the first 3 years is 6 percent per annum and for the next 2 years is 14 percent per annum. What is the sum?
Option 1: Rs. 17,000
Option 2: Rs. 15,000
Option 3: Rs. 14,000
Option 4: Rs. 16,500
Correct Answer: Rs. 16,500
Solution :
Given: The simple interest on a sum for 5 years is Rs. 7,590.
Let the principal be Rs. $P$.
We know, Simple interest = $\frac{\text{Principal × Time × Rate}}{100}$
The simple interest for the first 3 years at a 6% rate = $\frac{P\times 3\times 6}{100}=\frac{18P}{100}$.
The simple interest for the first 2 years at a 14% rate = $\frac{P\times 2\times 14}{100}=\frac{28P}{100}$
According to the question,
$\frac{18P}{100}+\frac{28P}{100}=7590$
⇒ $\frac{46P}{100}=7590$
⇒ $P=\frac{7590\times 100}{46}=$ Rs. 16,500
Hence, the correct answer is Rs. 16,500.
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