Question

Sum of money at simple interest amount to 1200 in 4 years and 1000 in two years what is the rate of interest

Answer 1

$\mathfrak{Step-By-Step\:Explanation:}$

Given :

Amount in 4 years =Rs.1200.

Amount in 2 years = Rs. 1000.

So

• SI of 2 years = 1200 - 1000 = Rs. 200.

Now we have :

• SI = Rs. 200.
• Time = 2 years.
• Amount = Rs. 1000.

$\boxed{\bold{Principle=Amount-SI}}\\\\\\\tt{=1000-200=Rs.\:800.}$

Let the rate be r % p.a.

$\boxed{\bold{SI=\dfrac{Principle\times Time\times Rate}{100}}}\\\\\\\implies\bold{200=\dfrac{800*2*r}{100}}\\\\\\\implies\bold{1600r=20000}\\\\\\\implies\bold{r=\dfrac{20000}{1600}}\\\\\\\implies\bold{r=\dfrac{25}{2}=12\dfrac{1}{2}\%.}\\\\\\\boxed{\boxed{\bold{Rate=12\dfrac{1}{2}\%}}}$

Answer 2

$\underline{\bold{Given}}$

Amount in 2 years = Rs.1000

Amount in 4 years = Rs.1200

Simple interest in 2 years = Rs.1200 - 1000 = Rs.200

We know that ,

Amount = principle + Simple interest.

So the principle is ,

Principle = Amount - SI

= Rs.1000 - 200 = Rs.800 .

Time = 2 years

let take the rate as r % .

we know that,

SI = $\frac{ P × r × t }{100}$

200 = $\frac{ 800 × r × 2 }{100}$

200 = 16 × r

$\frac{200}{16}$ = r

$\frac{25}{2}$ = r

12.5 % = r

$\therefore$ Rate of interest = 12.5 %.