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Easy

Question

# 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?

Hint:

### Frame 2 equations from the information provided and find the ratios.

## 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.

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