Question

the principal at a certain rate of interest Doubles in 5 years by simple interest in how many years the same principle with the same rate of interest becomes five times​

Answer 1

In 20 years the same principle with the same rate of interest becomes five times​

•Let Principle = x Rs & rate = r

•Time period = t

Case 1

• Final Amount = 2x Rs

•Principle = x Rs & rate = r

• t = 5 years

• Simple intrest = Final Amount -

Principle

• SI = 2x-x

• SI = x Rs

• (P×R×T)/100 = x

• x.R×5 = 100x

• R = 20 %

Case 2

• Final Amount = 5x Rs

•Principle = x Rs & rate = 20 %

• Time period = t years

• Simple intrest = Final Amount -

Principle

• SI = 5x-x

• SI = 4x Rs

• (P×R×T)/100 = 4x

• x×20×t= 400x

• t = 20 years

Answer 2

The time after which the amount becomes five times is 25 years

Step-by-step explanation:

Given as :

For simple interest

Statement I

The principal at a certain rate of interest Doubles in 5 years

Let The initial principal = Rs p

Amount after 5 year = A = 2 p

The rate of interest = r%

The time period = 5 years

∵ Interest =  Amount - principal

Or,  interest = 2 p - p = p

From simple interest method

S.I = $\dfrac{p\times R\times T}{100}$

Or,  p = $\dfrac{p\times R\times 5}{100}$

Or, R = $\dfrac{100}{5}$ = 20%

So, The rate of interest = 20%

Again

Statement II

The initial principal = Rs p

Amount after 5 year = A = 5 p

The rate of interest = r% = 20%

The time period = T

∵ Interest =  Amount - principal

Or,  interest = 5 p - p = 4 p

From simple interest method

S.I = $\dfrac{p\times R\times T}{100}$

Or,  5 p = $\dfrac{p\times 20\times T}{100}$

Or,  T = $\dfrac{500}{20}$

∴     T = 25 years

So, The time period = T = 25 years

Hence, The time after which the amount becomes five times is 25 years Answer