he population of a town is 5,00,000. The rate of increase is 20% per annum. Find the population at the start of the third year.

To find the population at the start of the third year, we need to apply the rate of increase for two consecutive years to the initial population.

Step 1: Calculate the population after the first year. The rate of increase is 20%, so the population will increase by 20/100 * 5,00,000 = 1,00,000. So, the population at the end of the first year is 5,00,000 + 1,00,000 = 6,00,000.

Step 2: Calculate the population after the second year. Again, the population will increase by 20%. This time, we apply the rate to the population at the end of the first year, which is 6,00,000. So, the increase is 20/100 * 6,00,000 = 1,20,000. So, the population at the end of the second year (which is the same as the population at the start of the third year) is 6,00,000 + 1,20,000 = 7,20,000.

So, the population at the start of the third year is 7,20,000.