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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