A certain sum invested at simple interest amounts to Rs. 8,411 in 3$$\frac 12$$​ years and to Rs. 9,776 in 6 years at thesame rate of interest per annum. What is the rate of interest per annum?

Correct option is C

Given :

Amount after 3$$\frac{1}{2}$$ years = Rs. 8,411
Amount after 6 years = Rs. 9,776
Simple Interest, same rate

Formula Used :

Simple Interest Amount
A = P$$\left(1 + \frac{RT}{100}\right)$$​​

Difference of amounts at Simple Interest is proportional to difference of time.

Solution :

Difference in amounts:
9776 - 8411 = 1365

Difference in time:
6 - 3.5 = 2.5 years

So, interest for 2.5 years = Rs. 1365

Interest for 1 year:
​$$= \frac{1365}{2.5}$$​= 546

Now, interest for 3.5 years:
= 54$$6 \times 3.5$$​ = 1911

Principal:
P = 8411 - 1911 = 6500

Now use SI formula:
​$$\text{SI for 1 year} = \frac{P \times R}{100}$$​​

546 =$$\frac{6500 \times R}{100}$$​​

R$$= \frac{546 \times 100}{6500}$$​​

R = 8.4% per annum