Question

A $5$ meter wide lane was paved with bricks of size \[20\text{ }cm\text{ }\times \text{ }15\text{ }cm\] . If the rate of bricks is \[Rs.750\] per \[1000\] and if the bricks worth \[Rs.49500\] were used for pavement, find the length of the lane.

Answer 1

Hint: Here we use the concept of area of the rectangle.
Area of rectangle = length $\times$ breadth

Complete step by step answer:
\[Rs.750\] represents the cost of \[1000\] bricks.
\[Rs.49500\] represents cost of ? bricks, which represents the total number of bricks used.
Therefore, the total number of bricks used is given as follows:
$\begin{align}
  & \dfrac{Total\text{ }\cos t\text{ }of\text{ }used\text{ }bricks}{\cos t\text{ }of\,1000\text{ }bricks}\times 1000\text{ }bricks \\
 & =\dfrac{49500}{750}\times 1000 \\
 & =66000 \\
\end{align}$
The total number of bricks used is $66000$.
Area occupied by the total number of bricks represents the area of the lane.
Therefore,
$\begin{align}
  & Area\text{ }of\text{ }lane=total\text{ n}umber\text{ }of\text{ }bricks\times area\text{ }of\text{ }each\text{ }brick \\
 & \Rightarrow l\times 5m=66000\times (20cm\times 15cm) \\
 & \Rightarrow l=\dfrac{66000\times (20cm\times 15cm)}{5m} \\
 & \Rightarrow l=\dfrac{66000\times (20cm\times 15cm)}{500cm} \\
 & \Rightarrow l=39600cm \\
 & \Rightarrow l=396m \\
\end{align}$

Therefore, length of lane is $396\,m$.

Note: In such type of questions which involves concept of plane figures, knowledge of formulae related to plane figures is needed. Follow up accordingly by assigning the data in the formula to get the required value.