*17. The length of a room is 20 m and to cover the floor of the room by carpet rupees 2160 is required. Had the breadth been 4 m less the cost of covering with carpet would have been rupees 1620. Find the area of the floor of the room.
Answers
Step-by-step explanation:
24 m
Let the length and breadth of the room be x m and y m respectively.
Cost of carpeting xym
2
= Rs. 120
Cost of carpeting x(y−4) m
2
= Rs (120−20)= Rs. 100
∴
xy
x(y−4)
=
120
100
⇒
y
y−4
=
6
5
⇒6y−24=5y⇒y=24m
Given : The length of a room is 20 m and to cover the floor of the room by carpet rupees 2160 is required.
Had the breadth been 4 m less the cost of covering with carpet would have been rupees 1620.
To Find: the area of the floor of the room.
Solution:
Length = 20 m
Breadth = x m
cost of carpet per sq m = y
Hence Total cost = 20xy = 2160
=> xy = 108
New breadth = x - 4 m
New cost = 20(x - 4)y = 1620
=> xy - 4y = 81
=> 108 - 4y = 81
=> 4y = 27
=> y = 27/4
xy = 108
=> x (27/4) = 108
=> x = 16
Area of the floor = 20x
= 20(16)
= 320 m²
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