Question : An amount of INR $P$ was put at simple interest at a certain rate for 4 years. If it had been put at a 6% higher rate for the same period, it would have fetched INR 600 more interest. What is the value of $2.5P$?
Option 1: INR 3,750
Option 2: INR 6,250
Option 3: INR 4,850
Option 4: INR 2,500
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Correct Answer: INR 6,250
Solution :
Let's denote the initial rate of interest as $r$, and the principal amount as $P$ [Given]. The time is given as 4 years.
The interest earned at the initial rate $r$ is $I=\frac{P×r×T}{100}$, where T is the time in years.
The interest earned at a 6% higher rate is $I'=\frac{P×(r+6)×T}{100}$
According to the question,
The difference in interest is INR 600:
⇒ $I'-I=600$
⇒ $\frac{P×(r+6)×T}{100}-\frac{P×r×T}{100}=600$
⇒ $\frac{P×r×T}{100}+\frac{P×6×T}{100}-\frac{P×r×T}{100}=600$
⇒ $\frac{P\times 6\times 4}{100}=600$
⇒ $P=\frac{600\times 100}{6\times 4}=2500$
Now, $2.5P=2.5\times 2500=6250$
Hence, the correct answer is INR 6,250.
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