Read the given information and statements carefully and decide which option is True with respect to the information.

If a sum of money is lent at simple interest, then the:

Statements:

1. Money gets doubled in 6 years if the rate of interest is 16%.

2. Money gets doubled in 5 years if the rate of interest is 18%.

Correct option is C

Given:

The sum of money is lent at simple interest.

Formula Used:

The formula for Simple Interest (SI) is:

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

where P is the principal amount, R is the rate of interest per annum, and T is the time in years.

Solution:

The total amount A after time T is:

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

To double the money, A = 2P, so:

2$$P = P \left( 1 + \frac{R \times T}{100} \right)$$​

​$$2 = 1 + \frac{R \times T}{100}$$​​

​$$\frac{R \times T}{100} = 1$$​

R × T = 100

Statement 1: Money gets doubled in 6 years if the rate of interest is 16%.

Using the formula R × T = 100, substituting T = 6:

​$$R \times 6 = 100$$​​

R =$$\frac{100}{6} \approx 16.67\%$$​

The rate is approximately 16.67%, not 16%. Hence, Statement 1 is False.

Statement 2: Money gets doubled in 5 years if the rate of interest is 18%.

Using the formula R $$\times T =$$​ 100, substituting T = 5:

​$$R \times 5 = 100$$​

​$$R = \frac{100}{5} = 20\%$$​

The rate should be 20%, not 18%. Hence, Statement 2 is False.

Both statements are False.