A sum of money lent out at simple interest amounts to Rs. 720 after 2 years and Rs. 1020 after a further period of 5 years. Find the principal.

Let the principal amount be P and rate of interest be R and time period be T

SI = $$\frac{PxRxT}{100}$$

When T = 2years , it is give that

P + $$\frac{PxRx2}{100}$$ = Rs 720..............(1)

when T = 7 years

P + $$\frac{PxRx7}{100}$$ = Rs 1020...................(2)

subtracting equation 1 from 2

$$\frac{PxRx5}{100}$$ = 300

As we can see that in 5 years the SI accumulated on a given principle is Rs 300 and we know that SI is same for every year, and hence we can conclude that:

SI for 2 years = Rs 120 .....................(3)

Using equation 1 and 3

P = 720 - 120

P = Rs 600