Question

# A sum of money lent out at simple interest amounts to Rs. 1240 in 4 years and Rs 1360 in 6 years. Find the sum and rate percent?

Hint:

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

## The correct answer is: 1000 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 = 4.

So, Simple interest for 4 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 = 1240 and .

On substitution, we get …(i)

Case Ⅱ

We calculate simple interest by the formula,

Here we have T = 6.

So, Simple interest for 6 years = SI =

Formula for total amount = A = P + SI,

We have A = 1360 and SI = .

On substitution, we get A = 1360 = p + …(ii)

Form (i) and (ii), we have

This can be written as

On cross multiplication, we get 13600 + 544R = 12400 + 744R

On rearranging the above equation, we get 200R = 1200

Divide on both sides by 200.

On dividing, we get R = 6%

Substitute R = 6% in (ii).

Then we get 1360 = p +

On simplifications, we get P = 1000.

So principal amount P = 1000 Rupees.

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