Question

Mrs. Jain wants to fence her rectangular kitchen garden on three sides with lengths 15m, 8m, and 8m. Find the cost of fencing it at the rate of Rs.12 per meter and leveling it at the rate of Rs.4 per square meter.

Answer 1

Hint: We solve this problem by first finding the total length of the garden that needs to be fenced. Then we multiply the obtained value with the rate per meter for fencing to find the cost of fencing. Then we find the area of the garden using the formula for the area of the rectangle as, $Area=\left( length \right)\times \left( breadth \right)$ and multiply it with the rate per square meter to find the cost of leveling.

Complete step-by-step solution:
We are given that fencing has to be done on the three sides of the rectangular kitchen garden with lengths 15m, 8m, and 8m.

We are given that cost of fencing is Rs.12 per meter.
As we need to fence only three sides, let us find the total length of the sides that needs to be fenced, that is equal to,
Total length = 15 + 8 + 8 = 31m.
As the cost for fencing is Rs.12 per meter,
Total Cost = Rate per meter $\times $ Total length to fence
So, we get
$\begin{align}
  & \Rightarrow 12\times 31 \\
 & \Rightarrow 372 \\
\end{align}$
So, the Cost of fencing is Rs.372.
We are also given that the cost of leveling the ground is Rs.4 per square meter.
So, to find the cost of leveling the ground we need to find the area of the garden.
Now, let us consider the formula for the area of the rectangle.
$Area=\left( length \right)\times \left( breadth \right)$
Using this formula, we get the area of garden as
 $\begin{align}
  & \Rightarrow Area=15\times 8 \\
 & \Rightarrow Area=120 \\
\end{align}$
So, the area of the garden is 120 square meters.
As the cost of the levelling is Rs.4 per square meter, the cost of levelling is
Total Cost = Rate per square meter $\times $ Area of garden
So, we get
$\begin{align}
  & \Rightarrow 4\times 120 \\
 & \Rightarrow 480 \\
\end{align}$
So, we get the cost of the levelling the garden as Rs.480.
Hence, we get the cost of fencing and leveling as Rs.372 and Rs.480.
Hence, answer is Rs.372 and Rs.480.

Note: There is a possibility of one making a mistake while solving this problem in the section of finding the cost for fencing. One might find the cost for fencing as below.
$\begin{align}
  & \Rightarrow Perimeter=2\left( l+b \right) \\
 & \Rightarrow Perimeter=2\left( 15+8 \right) \\
 & \Rightarrow Perimeter=2\left( 23 \right)=46 \\
\end{align}$
So, Cost = Rate per cm $\times $ Perimeter
$\Rightarrow \text{Cost}=12\times 46=552$
Then cost of fencing is Rs.552.
But it is wrong as we are fencing only three sides of the garden.