Question

The length of a room is 50% more than its breadth . The cost of carpeting the room at the rate of rupees38.50 and the cost of papering the walls at rupees 3.30m square is rupees 214.50 . If the room has 1 door of dimension 1m× 2m and 2 window each of dimension 1m× 1.5m , find the dimension of room

Answer 1

$\bf{\underline{\underline{Answer:}}}$

• Length of the room = 6 meters
• Breadth of the room = 4 meters
• Height of the room = 3.5 meters

$\bold{\underline {Given:}}$

• The length of a room is 50% more than its breadth
• The cost of carpeting the room at the rate of ₹ 38.50
• The cost of papering the walls at ₹ 3.30 m² is ₹ 214.50
• One dimension of the room = 1 m × 2 m
• Second dimension of the room = 1 m × 1.5 m

$\bold{\underline {To\:find:}}$

• The dimensions of the room =?

$\bf{\underline{\underline{Step\: by\: step= \:explanation:}}}$

Let the breadth of the room be $x$ metres .

As the length of the room is 50 % more than its breadth, length of the room = $\left (1 + \dfrac{50}{100}\right) \:of \:x \:meters = \dfrac{3}{2}x \:meters$

∴ The area of the floor of the room =$\left(\dfrac{3}{2}x \times x \right) m^2 = \dfrac{3x^2}{2}m^2.$

Cost of carpeting the room at the rate of ₹ 38. 50 m²

=₹$\left(\dfrac{3x^2}{2}\times 38.5 \right).$

According to given ,

$\dfrac{3x^2}{2}\times{38.5}=924\\ \\ \implies x^2 = \dfrac{924\times 2}{3 \times 38.5}\\ \\ \implies x^2 = 16\\ \\ \implies x = 4 \:\:\:\:\:\:( \therefore x \:can \:not \:be \:negative )$

Hence , the length of the room = $\dfrac{3}{2} {\sf\:x \:meters} = \dfrac{3}{2}\times 4$ metres = 6 metres

and its breadth = x metres = 4 metres .

Let the height of the room be $h$ metres , then

the surface area of all the walls of the room

= 2 ( length + breadth ) x height

$= 2(6 + 4) \times h \:m^2 \\ \\= 20 h\:m^2$ .

Area of one door = 1x 2 m² = 2 m² ,

area of two windows = 2 ( 1 x 1.5 ) m² = 3 m².

∴ Surface area to be papered

= surface area of walls - surface area of door and windows

= ( 20h - 2 - 3 ) m² = ( 20h- 5 ) m² .

∴ Cost of papering the walls at the rate of ₹ 3.30 m²

= ₹ ( 20h - 5 ) × 3.30 .

According to given $( 20h - 5 ) \times 3.30 = 214.50\\ \\ \implies 20h - 5 = \dfrac{214.50}{3.30}=65\\ \\ \implies 20h = 65 + 5 \\ \\ \implies 20h = 70 \\ \\ \bf \implies h = 3.5 .$

$\bf{Hence,\: the\: height \:of \:the\: room = 3.5 \:meters}$

Answer 2

Question :

The length of a room is 50% more than its breadth. The cost of carpeting the room at the rate of ₹38.50 m² is ₹924 and the cost of papering the walls at ₹3.30 m² is ₹214.50 . If the room has one door of dimensions 1 m × 2 m and two windows each of dimensions 1 m × 1.5 m, find the dimensions of the room.

Given :

• The length of a room is 50% more than its breadth.

• The cost of carpeting the room at the rate of ₹ 38.50

• The cost of papering the walls at ₹ 3.30 m² is ₹ 214.50

• One dimension of the room = 1 m × 2 m.

• Second dimension of the room = 1 m × 1.5 m.

To Find :

The dimensions of the room = ?

Solution :

Let the breadth of a room be (x)m. Then,

Length = x + 50 % of x

= x + 50/100 × x

= x + x/2

= 2x + x/2

= 3x/2

Area of floor = 924/38.50

=> l × b = 924 × 100/3,850

=> x × 3x/2 = 24

=> 3x²/2 = 24

=> x² = 24 × 2/3

=> x² = 16

=> x = √16

=> x = 4

Hence , breadth = 4m

length = 3 × 4/2

= 6m

Area of four walls = 1,320/5.50

=> 2(l+b) × h = 1,320 × 100/5.50

=> 2(6+4) × h = 240

=> 10h = 240/2

=> 10h = 120

=> h = 120/10

=> h = 12m

Final solution :

Dimensions of room are 6m × 4m × 12m .

Thank you.