A sum of money doubles itself in 8 years at a certain rate of simple interest. In how many years will it become 4 times the original amount at the same rate of interest?

Correct option is B

Given:

The sum doubles itself in 8 years
We need to find how many years it will take to become 4 times the original amount.

Formula Used:
1. Simple Interest:

​$$I = \frac{P \cdot R \cdot T}{100}$$​​

2. Relation Between Principal and Interest:

​$$\text{Total Amount} = P + I$$​​

Step-by-Step Solution:

Step 1: Determine the rate of interest (R):
Since the sum doubles itself in 8 years, the simple interest equals the principal:

I = P

Using the formula for simple interest:
​$$P = \frac{P \cdot R \cdot 8}{100}$$​​

Cancel P from both sides (since P > 0):

$$100 = R \cdot 8$$​​


Solve for R:

R = $$\frac{100}{8} = 12.5$$​ per annum


Step 2: Determine the time to become 4 times the original amount:
If the sum becomes 4 times the original amount, the total amount is:
​$$\text{Total Amount} = 4P$$​​


The interest earned in this case is:

I = 4P - P = 3P


Using the simple interest formula:
​$$3P = \frac{P \cdot R \cdot T}{100}$$​​


Cancel P from both sides:
​$$3 = \frac{R \cdot T}{100}$$​​


Substitute R = 12.5:
​$$3 = \frac{12.5 \cdot T}{100}$$​​


Solve for T:
​$$T = \frac{3 \cdot 100}{12.5} = 24 \, \text{years}$$​​