Question

A sum of money when kept at simple interest doubled in 8 year 4 monthd

Answer 1

$\boxed{\text{The complete question be :}}$

A sum of money when kept at simple interest doubled in 8 years and 4 months. Find the rate of interest per year.

$\underline{\underline{\bold{Solution :}}}$

Let, the amount of money be P rupees and rate of simple interest per annum be r %

Given, time ( t ) = 8 years 4 months

= 8 years + 4 months

= ( 8 + $\frac{4}{12}$ ) years

= ( 8 + $\frac{1}{3}$ ) years

= $\frac{(8*3)+1}{3}$ years

= $\frac{25}{3}$ years

So, simple interest in 8 years and 4 months with the rate of r % be

I = $\frac{\text{Ptr}}{100}$

⇒ I = $\dfrac{\text{P}*\frac{25}{3}*\text{r}}{100}$ rupees

⇒ I = $\dfrac{\text{Pr}}{12}$ rupees

So, total money ( P + I ) after 8 years and 4 months be

= P + $\dfrac{\text{Pr}}{12}$

= $\dfrac{\text{12P+Pr}}{12}$

Given that, the sum be doubled in 8 years and 4 months

⇒ $\dfrac{\text{12P+Pr}}{12} = 2\text{P}$

⇒ 12P + Pr = 12 * 2P

⇒ 12P + Pr = 24P

⇒ ( 24 - 12 ) P = Pr

⇒ 12P = Pr

⇒ r = 12 [ ∵ P ≠ 0 ]

$\therefore \text{the required rate of interest}$
$\text{be 12\% per year.}$

Answer 2

Answer:

Rate of interest = 12% per annum

Step-by-step explanation:

Let say sum of Money = P

Let say rate of interest = R % per Annum

Time = 8 year 4 month

=> Time = 8 year + 4/12 Years

=> Time = 100/12 Years

Sum of money got doubled = 2P

Simple interest = 2P -P = P

Simple interest = (P * R * Time)/100

=> P = (P * R * (100/12))/100

=> 12P = PR

=> 12 = R

Rate of interest = 12% per annum