Question

The cost of carpeting a room 18 metre with a carpet 75 cm width at Rs. 4.50 per metre is Rs. 810. The breadth of the room is (k – 0.5) metre. Find the value of k/8.

1. 0.5
2. 2
3. 1
4. 0.25

Answer 1

$\huge\tt\pink{ANSWER:-}$

Given

Length of the Room = 18m

breadth of the carpet = 75 cm

= in meter 0.75m

the cost of carpet Rs. 4.50 per meter is Rs. 810

then the length of carpet =

$\: \: \: \: = \frac{total \: cost}{cost \: per \: meter} \\ \: \: \: = \frac{810}{4.50} = 180m$

Now

$area \: of \: rectangle \: = length \: \times breadth \\ so \: putting \: the \: l \: and \: b \: of \: the \: carpet \: \\ in \: formula \\ \\ \: \: = 180 \times 0.75 \: = 135 {m}^{2}$

Area of the Room = Area of carpet

$length \: \times breadth \: of \: the \: room = 135 {m}^{2}$

$18m \: \times (k \: - 0.5)m \: = 135 {m}^{2} \\ k - 0.5 = \frac{135}{18} \\ k - 0.5 = 7.5 \\ k = 7.5 + 0.5 \\ k = 8$

Now, let's find the value of

$\frac{k}{8} \\ \\ putting \: the \: value \: of \: k \: in \: equation \\ \\ \frac{k}{8} = \frac{8}{8} = 1$

Hence Your Answer will be 1

Answer 2

Step-by-step explanation:

Given that : Length of room=18m

Breadth of carpet= 75cm= 0.75m

As the total cost of the carpet at the rate of Rs. 4.50/m is Rs. 810

So, Length of the carpet will be= \dfrac{\text{Total cost}}{\text{cost per metre}}

cost per metre

Total cost

= \dfrac{810}{4.50}

4.50

810

= 180m180m

As we know Area of rectangle = length × breadth

∴ Area of carpet = length of carpet × breadth of carpet

=180\times0.75180×0.75 = 135 m^{2}135m

2

Area of room = Area of carpet

Therefore,

Length of room × breadth of room = 135 m^{2}135m

2

⇒18m\times(k-0.5)m= 135m^{2}18m×(k−0.5)m=135m

2

⇒k-0.5=\dfrac{135}{18}k−0.5=

18

135

⇒k-0.5=7.5k−0.5=7.5

⇒k=7.5+0.5k=7.5+0.5

⇒k=8k=8

The value of k is 8