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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Note:
When we have an inequality with the symbols < or > , we use dotted lines to graph them. This is because we do not include the end point of the inequality.