​A certain sum of money amounts to 13/5 of itself in 10 years on simple interest. What is the rate of interest per annum? ​

Correct option is B

Given:

The sum of money amounts to $$\frac{13}{5}$$​ of itself in 10 years on simple interest.

Formula Used:

A = P + SI

A = $$P \left(1 + \frac{R}{100} \times T\right)$$​​

Where:

A is the amount after time t.

P is the principal (initial amount).

r is the rate of interest per annum.

t is the time in years.

Solution:

The amount after 10 years is $$\frac{13}{5}$$​ of the principal, so:

A = $$\frac{13}{5} \times P$$​​

Substituting into the simple interest formula:

​$$\frac{13}{5} \times P = P \left(1 + \frac{R}{100} \times 10\right)$$​​

​$$\frac{13}{5} \times P = P \left(1 + \frac{10R}{100}\right) \\ \ \\\frac{13}{5} = 1 + \frac{R}{10}$$​​

​$$\frac{13}{5} - 1 = \frac{R}{10} \\ \ \\ \frac{13}{5} - \frac{5}{5} = \frac{R}{10} \\ \ \\ \frac{8}{5} = \frac{R}{10}$$​​

R = $$\frac{8}{5} \times 10 = 16$$​​

The rate of interest per annum is 16%.

Thus, the correct option is (b) 16%