The amounts of certain sum of money with simple interest at certain rate of interest are Rs. 5440 in 3 years and Rs. 6440 in 5 years. Find the sum and rate of interest?

The correct answer is: 3951 Rupees

Complete step by step solution:
Let the sum of money = P and rate of interest = R
Case Ⅰ
We calculate simple interest by the formula, 
where P is Principal amount, T is number of years and R is rate of interest
We are given T = 3.
So, Simple interest for 3 years = 
Formula for total amount = A = P + SI,
where A is the total amount, P is the principal amount and SI is simple interest .
We have A = 5440 and .
On substitution, we get …(i)
Case Ⅱ
We calculate simple interest by the formula, 
Here we have T = 5.
So, Simple interest for 5 years = 
Formula for total amount = A = P + SI,
We have A = 6440 and .
On substitution, we get …(ii)
Form (i) and (ii), we have

This can be written as 
On cross multiplication, we get 6440 + 1932R = 54400 + 2720R
On rearranging the above equation, we get 788R + 10000
Divide on both the sides by 788.
On dividing, we get 
Substitute  in (ii).
Then we get 

On simplifications, we get P = 3950.9 which can be rounded to Rs 3951.
So principal amount = 3951 Rupees.