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Mathematics

A room is 13 m long and 9 m wide. Find the cost of carpeting the room with a carpet 75 cm wide at ₹ 12.50 per metre.

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Answer

Given,

Room length = 13 m

Room width = 9 m

Carpet width = 75 cm = 0.75 m

Cost of carpet = ₹ 12.50 per metre.

Floor area = Room length × Room width

= 13 × 9 = 117 m2.

Floor area = Carpet length × Carpet width

⇒117=Carpet length×0.75⇒Carpet length=1170.75⇒Carpet length=117×10075⇒Carpet length=117×43⇒Carpet length=39×4⇒Carpet length=156 m.\Rightarrow 117 = \text{Carpet length} \times 0.75 \\[1em] \Rightarrow \text{Carpet length} = \dfrac{117}{0.75} \\[1em] \Rightarrow \text{Carpet length} = \dfrac{117 \times 100}{75} \\[1em] \Rightarrow \text{Carpet length} = \dfrac{117 \times 4}{3} \\[1em] \Rightarrow \text{Carpet length} = 39 \times 4 \\[1em] \Rightarrow \text{Carpet length} = 156 \text{ m}.

Total cost = Carpet length × Rate per meter

= 156 × ₹ 12.50

= ₹ 1,950.

Hence, total cost = ₹ 1,950.

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