Question

10. A halt is 26 m long and 22 m broad. Find
the cost of carpeting the room with a carpet
75 cm broad at the rate of 4.50 per metre.​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• A halt is 26 m long and 22 m broad

• Carpet is 75 cm broad

• Rate of carpeting is 4.50 per metre

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Cost of carpeting the halt

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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• Let 'x' be the length of carpet required

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$\boxed { \bold { 1 \: cm = \dfrac {1 } { 100 } m } }$

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• $\bf 75 \: cm = 0.75 \: m$

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$\underline{ \underline{\bold{\texttt{Area of rectangle :}}}}$

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➠ l × b ⚊⚊⚊⚊ ⓵

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Where ,

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• l = Length

• b = Breadth

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Clearly the halt is rectangular thus it's area can be calculated by the formula to calculate area of rectangle

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$\underline{ \underline{\bold{\texttt{Area of halt :}}}}$

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• l = 26

• b = 22

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⟮ Putting the above values in ⓵ ⟯

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: ➜ l × b

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: ➜ 26 × 22

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: ➜ 572 sq. m ⚊⚊⚊⚊ ⓶

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• Hence the area that need to be carpeted is 572 sq. m

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$\underline{ \underline{\bold{\texttt{Area of carpet :}}}}$

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• Length = x

• Breadth = 0.75 m

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⟮ Putting the above values in ⓵ ⟯

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: ➜ l × b

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: ➜ x × 0.75

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: ➜ 0.75x sq. m ⚊⚊⚊⚊ ⓷

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The area of carpet with 'x' length will be the same as that of halt

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So,

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: ➜ 572 = 0.75x

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: ➜ $\sf x = \dfrac { 572 } { 0.75 }$

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: ➜ x ≈ 762.66

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$\underline{ \underline{\bold{\texttt{Cost of carpeting :}}}}$

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Length of carpet required × Rate of carpeting

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• Length of carpet required ≈ 762.66 m

• Rate of carpeting = 4.50 per m

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: ➜ 762.66 × 4.50

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: : ➨ Rs 3431.97 ≈ Rs 3432

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• Hence the cost of carpeting the halt is Rs 3431.97 ≈ Rs 3432