The cost of a table and a chair are in the ratio of 5 : 7. If the cost of chair and table is increased by 20% and 10% respectively, then what will be the new ratio? (Bank Recruitment, 2007)

### Concept & Percentage Increase in Ratios To find a new ratio after individual percentage increases, apply the multiplier $(1 + \frac{\text{increase}}{100})$ to the respective ratio components, paying very close attention to the order of the items. ### Step-by-Step Solution * **Initial Setup**: Let the original cost of a table be $5x$ and a chair be $7x$ (since Table : Chair = $5 : 7$). * **Apply Increases (Watch the order!)**: The problem states the cost of **chair** and **table** is increased by $20\%$ and $10\%$ **respectively**. This means: Chair increase = $20\%$ Table increase = $10\%$ * **Calculate New Costs**: New Table Cost = $5x \times (1 + \frac{10}{100}) = 5x \times 1.10 = 5.5x$ New Chair Cost = $7x \times (1 + \frac{20}{100}) = 7x \times 1.20 = 8.4x$ * **Find the New Ratio**: New ratio of Table to Chair = $5.5x : 8.4x$ Multiply by $10$ to remove decimals: $55 : 84$ ### Exam Strategy & Shortcut Just multiply the ratio parts by their respective growth factors: Table = $5 \times 1.1 = 5.5$ Chair = $7 \times 1.2 = 8.4$ Ratio = $5.5 : 8.4 = 55 : 84$. ### Common Pitfall Not paying attention to the inverted order in the second sentence. The prompt gives the ratio as Table:Chair, but lists the percentage increases as Chair then Table. If you blindly apply $20\%$ to the table and $10\%$ to the chair, you will get an incorrect ratio of $60 : 77$ (Option c). ### Final Answer Therefore, the correct answer is **55 : 84**.