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Question

The length of a room is 50 % more than its breadth. The cost of carpeting the room at the rate of Rs. 38.50/ m^2 is Rs. 924 and the cost of painting the walls at the rate of Rs. 5.50/ m^2 is Rs. 1320. Find the dimensions of the room.

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Solution

Let the length of room be a

Width = a + a/2 = 3a/2

Cost of carpeting = 924

Rate of carpeting = 38.5

Area of floor = Cost /Rate

= 924 / 38.5

= 24 m^2

Length *Width = 24 m^2

a*3a/2 = 24

=> 3a^2 = 48

=> a^2 = 16

=> a= 4 m

Length of room = 4 m

Width of room = 6 m

Now,

Cost of painting =1320

Rate of painting = 5.5

Area of four walls = Cost /Rate

=>2(Length +width) *Height = 1320/5.5

=> 2*10 * Height = 240

=> 20 *Height = 240

=> Height = 12 m

Dimension of room are 4m ×6m ×12 m

Width = a + a/2 = 3a/2

Cost of carpeting = 924

Rate of carpeting = 38.5

Area of floor = Cost /Rate

= 924 / 38.5

= 24 m^2

Length *Width = 24 m^2

a*3a/2 = 24

=> 3a^2 = 48

=> a^2 = 16

=> a= 4 m

Length of room = 4 m

Width of room = 6 m

Now,

Cost of painting =1320

Rate of painting = 5.5

Area of four walls = Cost /Rate

=>2(Length +width) *Height = 1320/5.5

=> 2*10 * Height = 240

=> 20 *Height = 240

=> Height = 12 m

Dimension of room are 4m ×6m ×12 m

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