The production of a company has ups and downs every year. The production 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 from the year 2008, approximately what will be the effect on production of the company in 2012?
(a)27\% increase
(b)32\% increase
(c)37\% increase
(d)42\% increase
(e)52\% increase
Answer
Answer (as printed): C
Explanation
Let the production in 2008 be 100 units. Then, $$\begin{aligned} \text { Production in } 2012 & =100 \times\left(1+\frac{15}{100}\right)^{2}\left(1-\frac{10}{100}\right)\left(1+\frac{15}{100}\right) \\ & =\left(100 \times \frac{23}{20} \times \frac{23}{20} \times \frac{9}{10} \times \frac{23}{20}\right)=136.88 . \\ \therefore \text { Increase in production } & =(136.88-100) \%=36.88 \% \approx 37 \% . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.