To understand the problem, we need to know the following facts:

• The price of an article increases by 25% every odd year


• The price of an article decreases by 20% in every even year

To calculate the percentage change for one year, we can use the following formula:

Percentage change = (New Value - Old Value) / Old Value * 100

For odd years, the new value is 1.25 times the old value, and for even years, the new value is 0.8 times the old value. Therefore, we can calculate the percentage change for one year as follows:

Percentage change in odd year = (1.25 - 1) / 1 * 100 = 25%
Percentage change in even year = (0.8 - 1) / 1 * 100 = -20%


To calculate the percentage change for 180 years, we need to know the number of odd and even years in 180 years. Since the starting year is not given, we can assume that the first year is an odd year.

Number of odd years = (180 + 1) / 2 = 90
Number of even years = 180 / 2 = 90

Now, we can calculate the percentage change for odd and even years using the formula we derived earlier and apply it for 90 odd years and 90 even years.

Percentage change for 90 odd years = 1.25^90 = 2,817,028,151,377.56%
Percentage change for 90 even years = 0.8^90 = 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Let x=100.....
1st yr==> x=100+(25/100)*100=125.....
2nd yr==> x=125-(20/100)*100=100
...
so after every 2 years price is equal to original price.
=> after 180 yrs , final value of x=180
so,% change after 180 yrs = 0 %