A sum of money doubles at simple interest in 5 years. In how many years will it become four times itself?

Correct option is C

Given:

A sum of money doubles in 5 years.

We need to find the time it takes for the sum to become four times itself.

Formula Used:

Simple Interest

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

Where:

P = Principal

R= Rate 

T = Time in years

SI = Amount - Principal

Solution:

Let the principal sum of money be P.

When the money doubles, the amount becomes 2P.

SI = 2P - P = P​​

P = $$\frac{(P × R × 5) }{ 100}$$​ (Since time is 5 years)

R = $$\frac{100 } 5$$​​

R = 20%

Now, we need to find the time (T) when the amount becomes four times the principal, i.e., 4P.

SI = Amount - Principal

SI = 4P - P = 3P (Substitute R = 20%)

3P =$$\frac{(P\times20 × T) }{ 100}$$​​

T =$$\frac{ (3 × 100) }{ 20}$$​​

T = 15 years

Alternate Method:

Concept Used:
In simple interest, the interest is directly proportional to time.
If principal becomes n times, interest = (n - 1)P

Solution:

If P→ 2P in 5 years, then SI = P in 5 years

To become 4 times → SI = 3P

Time for 3P interest = 3 × 5 = 15 years