Question

Choose the correct answer of the following question:

The cost of carpeting a room 15 m long with a carpet 75 cm wide, at ₹70 per metre, is ₹8400. The width of the room is

(a) 9 m (b) 8 m (c) 6 m (d) 12 m

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Width}\mathrm{of}\mathrm{the}\mathrm{carpet}=75\mathrm{cm}=0.75\mathrm{m}\mathrm{and}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{room}=15\mathrm{m} \\ \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{carpet}=\frac{\mathrm{Cost}\mathrm{of}\mathrm{carpeting}}{\mathrm{Rate}\mathrm{of}\mathrm{carpeting}}=\frac{8400}{70}=120\mathrm{m} \\ \mathrm{Now},\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{carpet}\mathrm{required}\mathrm{for}\mathrm{carpeting}=120\times 0.75{\mathrm{m}}^2 \\ \Rightarrow \mathrm{area}\mathrm{of}\mathrm{the}\mathrm{floor}=120\times 0.75{\mathrm{m}}^2 \\ \Rightarrow 15\times \mathrm{breadth}=120\times 0.75 \\ \Rightarrow \mathrm{breadth}=\frac{120\times 0.75}{15} \\ \mathrm{So},\mathrm{breadth}=6\mathrm{m} \end{gathered}$$

Hence, the correct answer is option (c).