What sum of money at simple interest,amount to Rs.800 in 4 years and amount to Rs.900 in 6 years.Find the principal value and rate of interest.

Given that the sum of money amounts to Rs.800 in 4 years and Rs.900 in 6 years.

The difference in the amount of money over the two periods is Rs.900 - Rs.800 = Rs.100.

This difference is the simple interest accrued over the difference in time, which is 6 years - 4 years = 2 years.

So, the simple interest for 2 years is Rs.100.

Therefore, the simple interest for 1 year (or the rate of interest per annum) would be Rs.100 / 2 = Rs.50.

Since the sum amounts to Rs.800 in 4 years, and we know that Rs.50 is the interest for 1 year, the interest for 4 years would be Rs.50 * 4 = Rs.200.

Therefore, the principal (the original sum of money) would be the total amount after 4 years (Rs.800) minus the interest for those 4 years (Rs.200), which equals Rs.800 - Rs.200 = Rs.600.

So, the principal is Rs.600 and the rate of interest is Rs.50 per year.