Question

28.
The cost of carpeting a room 18m long with a carpet 75cm wide at 45 paise per meter
is Rs 81. The breadth of the room is
(a) 7m
(b) 7.5m
(C) 8m
(d) 8.5
​

Answer 1

Correct question:-

The cost of carpeting a room 18m long with a carpet 75 cm wide at Rs. 45 per meter is Rs 810. The breadth of the room is:

(a) 7 m

(b) 7.5 m

(C) 8 m

(d) 8.5 m

Answer:-

The breadth of the room is 7.5 m.

Explanation:-

Given :

Length of room = 18 m

Width of the carpet => 75 cm = 0.75 m

Cost of carpeting at the rate of Rs. 45 per meter = Rs. 810

Therefore, Length of the carpet = Total cost / Rate of carpeting per metre

$= > Length = \dfrac{810}{4.5} \: m$

$= > Length = \dfrac{810 \times 10}{45} \: m$

$= > Length = 18 \: m$

Now, we know the length of the room.

And the carpet is covering the whole room, So:-

Area of carpet = Area of room

Now, We will find the area of the carpet. As it is a rectangular room, the carpet is also in the same shape. As we know, the formula of the area of rectangle is = (Length × Breadth) sq. unit

$= > Area = (18 \times 0.75) \: {m}^{2}$

$= > Area = 135 \: {m}^{2}$

Hence, the area of the carpet or the room is 135 m.

Therefore, Breadth of room = Area of the room/ Length of the room

$= > Breadth = \dfrac{Area}{Length}$

$= > Breadth = \dfrac{135}{18} \: m$

$= > Breadth = 7.5 \: m$

Hence, The breadth of the room is 7.5 m.