Question

The length of a room is 50 per cent more than it's breadth the cost of carpeting the room at the rate of rupees 38.50m square is rupees 924 and the cost of painting the walls at the rate of rupees 5.50 per meter square is rupees 1,320 find the dimensions of the room.

Answer 1

Length of room=L
Breadth of room=B
Height of room=H
Since L is 50% more than breadth,
L=2B - - - - - - - - - (1)

Carpeting=₹924 @ ₹38.50/m²
Area of the room floor=924/38.50=23.75m²
L*B=23.75 - - - - - - - - - - - (2)
Put (1) in (2),
2B*B=23.75
2B²=23.75
B²=11.875
$b = \sqrt{(11.875)}$
B=3.446m
Hence L=2*3.446
L=6.892m


Painting the walls=₹1320 @ ₹5.50/m²
Area of four walls=1320/5.50=240m²
(L*H) + (B*H) + (L*H) + (B*H) = 240
2(L*H)+2(B*H)=240
2[(L*H)+(B*H)]=240
(L*H)+(B*H) =120
H(L+B)=120
H*(6.892+3.446)=120
H*10.338=120
H=120/10.338
H=11.608m

Hence dimensions of the room are
Length=L=6.892m
Breadth=B=3.446m
Height=H=11.608m

Answer 2

Length of room=L

Breadth of room=B

Height of room=H

Since L is 50% more than breadth,

L=2B - - - - - - - - - (1)

Carpeting=₹924 @ ₹38.50/m²

Area of the room floor=924/38.50=23.75m²

L*B=23.75 - - - - - - - - - - - (2)

Put (1) in (2),

2B*B=23.75

2B²=23.75

B²=11.875

b = \sqrt{(11.875)}b=(11.875)​ 

B=3.446m

Hence L=2*3.446

L=6.892m

Now,

Painting the walls=₹1320 @ ₹5.50/m²

Area of four walls=1320/5.50=240m
²
(L*H) + (B*H) + (L*H) + (B*H) = 240

2(L*H)+2(B*H)=240

2[(L*H)+(B*H)]=240

(L*H)+(B*H) =120

H(L+B)=120

H*(6.892+3.446)=120

H*10.338=120

H=120/10.338

H=11.608 m

Hence dimensions of the room are as follows:-

Length=L=6.892 m

Breadth=B=3.446 m

Height=H=11.608 m