Question

The production of a company has ups and downs every year. The productions increases for two consecutive years consistently by 15% and in the third year it decreases by 10% . Again in the next two years it increases by 15% each year and decreases by 10% in the third year. If we start counting form the year 1998, approximately what will be the effect on production of the company in 2002 ?

Answer 1

Let the production be 100 units.

The total time is $2002-1998=4yrs$.

So, the production increases by 15% over a time of 2yrs.

$\therefore$ The production after 2yrs.=$Initialamount\times {(1+rate)}^{time}=100\times {(1+\frac{1}{15})}^2$ units=$132.25$ units.

In the third year the rate is -10% since the production decreases.

$\therefore$ The production after 1yr.=$132.25(1-\frac{10}{100})$ units=$119.025$ units.

In the next year the production will increase by 15%.

$\therefore$ The production after 1yr.=$119.025(1+\frac{15}{100})$ units=$136.9$ units$\approx$$137$ units.

$\therefore$ The production will increase by$(137-100)$units=$37$ units.

Since the initial amount of units was$100$,

the production will increase by $37$%.