A sum was invested at a certain rate of simple interest per annum for 2 years. Had it been invested at 3% per annum more rate than the existing rate, the simple interest accrued in the 2 years would have been ₹240 more. The sum invested was:

Correct option is B

Given:

Difference in simple interest = ₹240

Time = 3 years

Formula Used:

Simple Interest = $$\frac{P \times R \times T}{100}$$​​

Solution:

Let the rate of interest be r

Then interest = $$\frac{P \times r \times 2}{100}$$​​

Interest when rate is increased by 3%

​$$= \frac{P \times (r+3) \times 2 }{100}$$​​

Difference is ₹240

​$$\frac{P \times (r+3) \times 2 }{100} - \frac{P \times r \times 2}{100} = 240$$​​

​$$\frac{2Pr}{100} - \frac{2Pr}{100} + \frac{6P}{100}= 240$$​​

​$$\frac{6P}{100}= 240$$​​

​$$P = \frac{240 \times 100}{6}= ₹4000$$​​