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 the total production (in tonnes) of Company A to the total sales (in tonnes) of Company A ?

### Concept & Ratio of Aggregates Calculate the sum of all values in the first set and the sum of all values in the second set independently, then express their relation in simplest fractional form. $$ \text{Ratio} = \frac{\sum \text{Production}_A}{\sum \text{Sales}_A} $$ ### Step-by-Step Solution * Calculate the total production of Company A across all years: * Total Production = $750 + 800 + 600 + 550 + 700 + 650 = 4050$ tonnes. * Calculate the total sales of Company A across all years: * Total Sales = $300 + 550 + 450 + 400 + 500 + 550 = 2750$ tonnes. * Form the ratio of Total Production to Total Sales: * Ratio = $4050 : 2750$. * Simplify by dividing both sides by $10$: $405 : 275$. * Simplify further by dividing both sides by $5$: * $405 \div 5 = 81$ * $275 \div 5 = 55$ * The final simplified ratio is $81 : 55$. ### Exam Strategy & Shortcut End digits ending in zero make for quick addition. Once you establish the initial ratio of $4050 : 2750$, dropping the zero leaves $405 : 275$. Since both end in $5$, dividing by $5$ immediately gives $81 : 55$, circumventing more complex simplification tests. ### Common Pitfall A common pitfall is reversing the order requested in the prompt (finding Sales to Production instead of Production to Sales), or making arithmetic errors when summing the six data points. ### Final Answer Therefore, the correct answer is **81 : 55**.