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 ratio of production of Company B (in tonnes) in the year 2006 to production of Company B (in tonnes) in the year 2008 ?

### Concept & Ratio Derivation To find the required ratio, determine the exact values for Company B in the specified years using the proportions provided in the table linked to the absolute values in the graph. ### Step-by-Step Solution * **Step 1: Find Production of Company B in 2006** * The graph shows Company A's production in 2006 is $750$ tonnes. * The table shows the ratio of Production (A : B) in 2006 is $5 : 4$. * Production of Company B in 2006 = $(\frac{750}{5}) \times 4 = 150 \times 4 = 600$ tonnes. * **Step 2: Find Production of Company B in 2008** * The graph shows Company A's production in 2008 is $600$ tonnes. * The table shows the ratio of Production (A : B) in 2008 is $3 : 4$. * Production of Company B in 2008 = $(\frac{600}{3}) \times 4 = 200 \times 4 = 800$ tonnes. * **Step 3: Calculate the Ratio** * Required Ratio = Production B in 2006 : Production B in 2008 * Ratio = $600 : 800$. * Simplify by dividing both by $200$: * Ratio = $3 : 4$. ### Exam Strategy & Shortcut Calculate the multipliers directly. In 2006, the multiplier for the ratio is $\frac{750}{5} = 150$. So, B is $150 \times 4$. In 2008, the multiplier is $\frac{600}{3} = 200$. So, B is $200 \times 4$. The ratio is simply $(150 \times 4) : (200 \times 4)$, which immediately simplifies to $150 : 200$ or $3 : 4$. ### Common Pitfall A frequent error is misreading the years or using the sales ratio instead of the production ratio, which would yield entirely different intermediate values and an incorrect final ratio. ### Final Answer Therefore, the correct answer is **3 : 4**.