Question

a principle amount of money at simple interest amounts to rupees 915 in 3 years and to rupees 945 in 4 years. Calculate the principle amount?

Answer 1

There is a formula for this:
Rate=Difference of Amounts of two consecutive years x 100/Preceding yrs amount x 1
Rate=(945-915) x 100/915 x1
Rate=(30 x 100)/915
Rate=3000/915=3.28%

Answer 2

Let P be the Principal and r be the rate of interest.

Since the principal amounts to 915 in 3 years, simple interest would be 915 - P

Similarly, Since the principal amounts to 945 in 4 years, simple interest would be 945 - P

915 - P = 3Pr/100, Since SI = Pnr/100, where n = 3.
945 - P = 4Pr/100,  where n = 4.

3Pr = 91500 - 100P ----------------1
4Pr = 94500 - 100P ---------------2

Subtracting equation 1 from equation 2, we get

Pr = 3000

Substituting the value of Pr = 3000 in equation 2

4 * 3000 = 94500 - 100P
12000 = 94500 - 100P
100P = 82500
P = 825.

Principal Amount = Rs 825.

Check for the solution:

Substitute the value of P in Pr = 3000

r = 3000/825 = 3.636%

SI(3) = 3 * 3000 * 3.636 / 100 = 90

Amount after 3 years = 825 + 90 = Rs 915

Similarly, SI(4) = 4 * 3000 * 3.636 / 100 = 120

Amount after 4 years = 825 + 120 = Rs 945

Thus P = Rs 825 and r = 3.636%