Question

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The carpet for a room 6.6 m by 5.6 m costs 3960 and it was made from a roll 70 cm wide. Find
the cost of the carpet per metre.

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Answer 1

${\large{\pmb{\sf{\underline{About \; question...}}}}}$

☀ Correct question : The carpet for a room 6.6 m by 5.6 m costs Rupees 3960 and it was made from a roll 70 cm wide. Find the cost of the carpet per metre.

☀ Understanding the question : This question says that we have to find out the cost of the carpet per metre. The cost of carpet is Rupees 3960. And the carpet is made from a roll of breadth 70 cm. And the carpet is set in room of dimensions 6.6 m by 5.6 m. Means it's length and breadth is 6.6 m and 5.6 m respectively.

${\large{\pmb{\sf{\underline{Given \; that...}}}}}$

✹ Length of the carpet = 6.6 m

✹ Breadth of the carpet = 5.6 m

✹ It's cost as given = Rupees 3960

✹ Breadth of roll = 70 cm

${\large{\pmb{\sf{\underline{To \; find...}}}}}$

✹ The cost of the carpet per metre.

${\large{\pmb{\sf{\underline{Solution...}}}}}$

✹ The cost of the carpet per metre = Rupees 75

${\large{\pmb{\sf{\underline{Using \; concept...}}}}}$

✹ Formula to find area of rectangle.

✹ Formula to convert cm into m.

${\large{\pmb{\sf{\underline{Using \; concept...}}}}}$

✹ Area of rectangle = Length×Breadth

✹ cm into m = 1/100

${\large{\pmb{\sf{\underline{Full \; Solution...}}}}}$

~ Firstly let us convert cm into m. As the length and breadth of the room are given in metres and the roll's breadth is given in centimetres. So, there is a need to convert m into cm or cm into m. Let us convert cm into m. Let's convert..!

$:\implies \sf 1 \: cm \: = 1/100 \: m \\ \\ :\implies \sf 70 \: cm \: = 70/100 \\ \\ \implies \sf 7/10 \\ \\ :\implies \sf 0.7 \: metres$

• Henceforth, 0.7 metres is the breadth of the roll.

~ Now let's find the area of the room. By using formula to find area of rectangle we have to find area of room.

$:\implies \sf Area \: of \: rectangle \: = Length \times Breadth \\ \\ :\implies \sf Area \: of \: rectangle \: = 6.6 \times 5.6 \\ \\ :\implies \sf Area \: of \: rectangle \: = 36.96 \: metres^{2}$

• Henceforth, 36.96 m² is the area of the room.

~ Now let's find the cost of carpet per metre square.

$:\implies \sf Cost \:of \: carpet \: per\: metre \: square \: = 3960/36.96 \\ \\ :\implies \sf Cost \:of \: carpet \: per\: metre \: square \: = 107.14 \: Rupees$

• Henceforth, 107.14 Rupees is the cost of carpet per metre square.

~ Now let's find the cost of carpet per metre.

$:\implies \sf Cost \:of \: carpet \: per\: metre \: = 0.7 \times 107.14 \\ \\ :\implies \sf Cost \:of \: carpet \: per\: metre \: = 75 \: Rupees$

• Henceforth, rupees 75 is the cost of carpet per metre.