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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