Question
A certain sum at simple interest amounts to Rs. 3,900 in 3 years and Rs. 4,500 in 5 years. Find the sum and rate of interest per annum.
Hint:
Frame 2 equations from the information provided and find the ratios.
The correct answer is: 3000 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 is Principal amount, is number of years and is rate of interest
We are given T = 3.
So, Simple interest for 3 years = 
Formula for total amount = A = P + SI,
where is the total amount, is the principal amount and is simple interest .
We have A = 3900 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 = 4500 and .
On substitution, we get 
…(ii)
Form (i) and (ii), we have
This can be written as 
On cross multiplication, we get 45000 + 1350R = 39000 + 1950R
On rearranging the above equation, we get 600R = 6000
Divide on both sides by 600.
On dividing, we get R = 10%
Substitute R = 10% in (ii).
Then we get 4500 = p + 
On simplifications, we get P = 3000.
So principal amount = 3000 Rupees.
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