Directions: Study the following information and answer the questions that follow : The graph given below represents the production (in tonnes) and sales (in tonnes) of Company A from 2006 to 2011. [Graph Data of Company A] | Year | Production (in tonnes) | Sales (in tonnes) | |---|---|---| | 2006 | 750 | 300 | | 2007 | 800 | 550 | | 2008 | 600 | 450 | | 2009 | 550 | 400 | | 2010 | 700 | 500 | | 2011 | 650 | 550 | The table given below represents the ratio of the production (in tonnes) of Company A to the production (in tonnes) of Company B, and the ratio of sales (in tonnes) of Company A to the sales (in tonnes) of Company B. | Year | Production (A : B) | Sales (A : B) | |---|---|---| | 2006 | 5 : 4 | 2 : 3 | | 2007 | 8 : 7 | 11 : 12 | | 2008 | 3 : 4 | 9 : 14 | | 2009 | 11 : 12 | 4 : 5 | | 2010 | 14 : 13 | 10 : 9 | | 2011 | 13 : 14 | 1 : 1 | What is the average production of Company B (in tonnes) from the year 2006 to the year 2011?

### Concept & Proportional Scaling and Averages First, find the exact values for Company B using the given ratio of $A : B$ and the known value of $A$. Then, find the average of the derived data set. $$ \text{Value of B} = \frac{\text{Value of A}}{\text{Ratio part of A}} \times \text{Ratio part of B} $$ ### Step-by-Step Solution * Calculate the production of Company B for each year: * **2006:** Ratio A:B is $5:4$. Prod A = $750$. Prod B = $(\frac{750}{5}) \times 4 = 150 \times 4 = 600$. * **2007:** Ratio A:B is $8:7$. Prod A = $800$. Prod B = $(\frac{800}{8}) \times 7 = 100 \times 7 = 700$. * **2008:** Ratio A:B is $3:4$. Prod A = $600$. Prod B = $(\frac{600}{3}) \times 4 = 200 \times 4 = 800$. * **2009:** Ratio A:B is $11:12$. Prod A = $550$. Prod B = $(\frac{550}{11}) \times 12 = 50 \times 12 = 600$. * **2010:** Ratio A:B is $14:13$. Prod A = $700$. Prod B = $(\frac{700}{14}) \times 13 = 50 \times 13 = 650$. * **2011:** Ratio A:B is $13:14$. Prod A = $650$. Prod B = $(\frac{650}{13}) \times 14 = 50 \times 14 = 700$. * Total Production of Company B = $600 + 700 + 800 + 600 + 650 + 700 = 4050$ tonnes. * Average Production = $\frac{4050}{6} = 675$ tonnes. ### Exam Strategy & Shortcut To quickly sum the series $600, 700, 800, 600, 650, 700$, choose a base like $600$. The deviations are $0, +100, +200, 0, +50, +100$. Sum of deviations = $450$. Average deviation = $\frac{450}{6} = 75$. Average = $600 + 75 = 675$. This avoids adding large numbers. ### Common Pitfall A common error is using the Sales ratio instead of the Production ratio to find Company B's values, which fundamentally changes all derived figures. ### Final Answer Therefore, the correct answer is **675**.