Question

The dimensions of rectangle field are 50m and 40 m flower bed is prepared inside this field leaving a gravel path of uniform width all around the flower bed the total cost of laying the flower bed and gravelling the path at rs 30 and Rs 20 per square m respective is rs 52000find the width of gravel path

Answer 1

width of gravel path is 5m.
40 you can't take ....

Answer 2

Answer:

The width of the graval path is 5 metres.

Step-by-step explanation:

Given:

The length of the park is 50m

The breadth of the park is 40m

Gravel path is built inside the park at its periphery;

Let us assume that the width of the path is a meter.

The total external area of the park is 50 × 40 = $2000^{2}$

Width of the path is a meter

Length of the flowerbed is 50 –a-a=50-2a  

Breadth of the flowerbed is 40 –a-a=40-2a  

Area of the flower bed inside the park = Length of the flowerbed x Breadth of the flowerbed

50-2a × 40-2a = Area of the flowerbed inside the park

Area of the flowerbed inside the park= 2000-180a+ $4 a^{2}$

Area of the gravel of T shaded region side = 100a

Area of the gravel of W shaded region side = 80a – $4 a^{2}$

Total area of the gravel path = (180a – $4 a^{2}$)

The total cost of the flowerbed and gravel path cost =Rs. 54000

Cost of Flowerbed = Rs.30 ×(2000-180a+$4 a^{2}$)

Cost of the gravel path = Rs.20 ×(180a – $4 a^{2}$)

Therefore total cost = Cost of Flowerbed + Cost of the gravel path

54000 = Rs.30 ×(2000-180a+$4a^2$ )+  Rs.20 ×(180a – $4 a^{2}$)

After equating, we get

$40 a^{2}$-1800a+8000  

$a^{2}$-45a+200  

(x-5)(x-40)  

a = 5 and 40 m, now a cannot be 40 as it exceeds park length, therefore the correct width is 5m

The width of the gravel path is 5m.