A certain sum of money becomes ₹1000 in 2 years and ₹1100 in 4 years at simple rate of interst. The rate of interst per annum is

Correct option is B

Given:

Amount after 2 years = ₹1000

Amount after 4 years = ₹1100

Interest type = Simple Interest

Formula:

Simple Interest (SI) = (Principal × Rate × Time) / 100

Rate (R) = (100 × Interest) / (Principal × Time)

Solution:

Difference in amount from year 2 to year 4 = ₹1100 - ₹1000 = ₹100

So, interest for 2 years = ₹100 => Interest per year = ₹50

Therefore, interest for first 2 years = ₹100 => Principal = ₹1000 - ₹100 = ₹900

Now apply the formula:

$$I = \frac{P \cdot R \cdot T}{100} \Rightarrow 50 = \frac{900 \cdot R \cdot 1}{100} \\\ \\\Rightarrow 50 = \frac{900R}{100} \Rightarrow 50 = 9R \\\ \\\Rightarrow R = \frac{50}{9} = 5\frac{5}{9}\% \\[10pt]$$​​​

Final Answer: $$5\frac{5}{9}\% \\[10pt]$$​