If the annual rate of simple interest increases from 8% to $$12\frac{1}{2}$$​%, a person's yearly income from interest increases by ₹369 then what is the principal amount of his investment?

Correct option is D

Given:

Initial simple interest rate = 8% per annum

New simple interest rate = $$12\frac{1}{2}\%$$​ per annum = 12.5% per annum

Increase in yearly interest = ₹369

Time = 1 year

Concept Used:

The simple interest formula:

$$\text{SI} = \frac{P \times R \times T}{100}$$

Solution:

​$$\frac{P \times 12.5}{100} - \frac{P \times 8}{100} = 369$$​​

​$$\frac{P (12.5 - 8)}{100} = 369$$​​

​$$\frac{P \times 4.5}{100} = 369$$​​

P = $$\frac{369 \times 100}{4.5}$$​​

P =$$\frac{36900}{4.5} = 8200$$​

The principal amount is ₹8,200.