Question : The simple interest on a sum of money in 6 years at the rate of 15% per annum is INR 1,440 less than the simple interest accrued on the same sum in 9 years at 18% per annum. What is the sum of money (in INR)?
Option 1: 1800
Option 2: 2000
Option 3: 2700
Option 4: 2400
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Correct Answer: 2000
Solution :
Let the principal be $P$.
Simple interest
1st
$=\frac{\text{Principal × Rate × Time}}{100}$$=\frac{P\times 15\times 6}{100}=\frac{90P}{100}$
And, Simple interest
2nd
$=\frac{P\times 18\times 9}{100}=\frac{162P}{100}$
According to the question,
Simple interest
1st
= Simple interest
2nd
– 1440
⇒ $\frac{90P}{100}=\frac{162P}{100}-1440$
⇒ $\frac{162P-90P}{100}=1440$
⇒ $72P=144000$
⇒ $P=\frac{144000}{72}$ = INR 2000
Hence, the correct answer is 2000.
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