The total cost of flooring a room at ₹ 8.50 per square metre is ₹ 510. If the length of the room is 8 m, its breadth is (R.R.B. 2006)

### Concept & Formula The area of a room can be found by dividing the total cost of flooring by the cost per square unit. Once the area is known, use the area formula to find the missing dimension. $$ \text{Area} = \frac{\text{Total Cost}}{\text{Rate per sq. unit}} $$ $$ \text{Area} = \text{Length} \times \text{Breadth} $$ ### Step-by-Step Solution * **Given:** Total Cost = ₹ $510$, Rate = ₹ $8.50\text{ per sq. m}$, Length = $8\text{ m}$. * **Step 1:** Calculate the area of the room. $\text{Area} = \frac{510}{8.50}$ * To simplify the division, multiply numerator and denominator by 10. $\text{Area} = \frac{5100}{85}$ $\text{Area} = 60\text{ sq. m}$ * **Step 2:** Use the area to find the breadth. $60 = 8 \times \text{Breadth}$ $\text{Breadth} = \frac{60}{8}$ $\text{Breadth} = 7.5\text{ m}$ ### Exam Strategy & Shortcut To quickly divide $510$ by $8.5$, notice that $8.5 \times 2 = 17$. So, $\frac{510}{8.5} = \frac{510 \times 2}{17} = \frac{1020}{17} = 60$. Then dividing $60$ by $8$ gives $7.5$. ### Common Pitfall Students sometimes multiply the total cost by the rate instead of dividing, resulting in an unrealistically large area. Always verify units: $\frac{\text{Cost}}{\text{Cost/Area}} = \text{Area}$. ### Final Answer Therefore, the correct answer is **7.5 m**.