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?

### Concept & Formula This problem tests the application of successive percentage changes over a specified timeline. When a value undergoes multiple percentage changes sequentially, we use the compound growth multiplier formula: $$ \text{Final Value} = \text{Initial Value} \times \left(1 \pm \frac{R_1}{100}\right) \times \left(1 \pm \frac{R_2}{100}\right) \times \dots $$ ### Step-by-Step Solution * **Determine the Timeline:** Starting from the end of 2008 (Base Year / Year 0). * Year 1 (End of 2009): Increase of $15\%$ * Year 2 (End of 2010): Increase of $15\%$ * Year 3 (End of 2011): Decrease of $10\%$ * Year 4 (End of 2012): Increase of $15\%$ Note: The pattern repeats, but we only need to calculate up to 2012, which is 4 years of changes. * **Set up the Multipliers:** * $+15\% \rightarrow 1.15$ * $-10\% \rightarrow 0.90$ * **Calculate the Net Effect:** $$ \text{Net Multiplier} = 1.15 \times 1.15 \times 0.90 \times 1.15 $$ * **Execute the Multiplication:** $$ 1.15 \times 1.15 = 1.3225 $$ $$ 1.3225 \times 0.90 = 1.19025 $$ $$ 1.19025 \times 1.15 = 1.3687875 $$ * **Convert Multiplier to Percentage:** A multiplier of $1.3687875$ represents an overall increase of approximately $36.88\%$. Rounding to the nearest whole number given in the options, we get a $37\%$ increase. ### Exam Strategy & Shortcut **Effective Percentage Approximation:** Use the successive percentage formula: $A + B + \frac{AB}{100}$ 1. Combine the first two $15\%$ increases: $15 + 15 + \frac{15 \times 15}{100} = 30 + 2.25 = 32.25\%$ 2. Combine this $32.25\%$ increase with the $10\%$ decrease: $32.25 - 10 - \frac{32.25 \times 10}{100} = 22.25 - 3.225 = 19.025\%$ 3. Combine this $19.025\%$ increase with the final $15\%$ increase: $19.025 + 15 + \frac{19.025 \times 15}{100} = 34.025 + 2.85375 = 36.87875\%$ Approximating this yields $37\%$. Breaking it into pairs avoids dealing with large four-term decimal multiplications. ### Common Pitfall The most common error is miscounting the number of years between 2008 and 2012. Students often calculate for 5 years instead of 4, incorrectly adding the final $-10\%$ drop to their sequence, which yields a drastically lower and incorrect answer. Always map out the year-to-year timeline explicitly. ### Final Answer **Therefore, the correct answer is 37% increase.**