the length of a room is 50% more than its breadth the cost of carpeting the room at the rate of rupees 38.5 M square is rupees 924 and the cost of painting the wall @ rupees 5.50 per metre square is rupees 1320 find the dimension of the room
Answers
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 .