Question

A carpet is $30\ m\ 75\ cm$ long and $80\ cm$ wide. Find the cost at $Rs.150$ per square metre.

Answer 1

Hint: Here, we are given length and width in metre and centimeter so, first of all we will convert them into a common unit either metre or centimeter using $1\ cm=\dfrac{1}{100}\ m$ or $1\ m=100\ cm$, Then we will find the area of carpet using the formula of area of rectangle i.e. $\text{Area of rectangle}=\left( length\times width \right)\ {{m}^{2}}$ and then from that we will find the cost of carpet per square using unitary multiplication method. Thus, in this way we will find the cost of carpet per square meter.

Complete step-by-step answer:
In question we are given the length and width of carpet i.e. $30\ m\ 75\ cm$ and $80\ cm$ respectively, as well as we are given that the cost per square meter is $Rs.150$ and we are asked to find the total cost, so first of all we will convert all the values of length and width into one unit system i.e. either metric or centimeter. So, conversion of metre to centimeter can be given as,
$1\ m=100\ cm$ or $1\ cm=\dfrac{1}{100}\ m$
Here, we will convert them into metre for simplicity, so, the conversion can be done as,
$length\ \left( l \right)=30\ m\ 75\ cm=30\ m+\dfrac{75}{100}\ m$
$\Rightarrow length\ \left( l \right)=30\ m+0.75\ m=30.75\ m$
$width\ \left( w \right)=80\ cm=\dfrac{80}{100}\ m$
$\Rightarrow width\ \left( w \right)=0.8\ m$
Now, the area of carpet can be given as area of rectangle as the carpet is in the shape of rectangle which can be seen from figure,

Now, we know that area of rectangle can be given as,
$\text{Area of rectangle}=\left( length\times width \right)\ {{m}^{2}}$
Using this, area of carpet can be given as,
$\text{Area of carpet}=length\times width=\left( l\times w \right)\ {{m}^{2}}$
Now, on substituting the values we will get,
$\text{Area of carpet}=30.75\times 0.8=24.6\ {{m}^{2}}$
Now, we are given that cost per square meter is $Rs.150$, so we can say that if the cost of one square meter is $Rs.150$, then cost of $24.6\ {{m}^{2}}$ will be x and we can solve this by unitary method which can be given as,
$\begin{align}
  & \text{cost of }1\ {{m}^{2}}\ =\ Rs.150 \\
 & \text{cost of 24}\text{.6}\ {{m}^{2}}\ =\ x \\
\end{align}$
On solving we will get,
$\ x\times 1\ =\ 150\times 24.6$
$\ x\ =\ 150\times 24.6=3690$
Thus, we can say that the cost of $24.6\ {{m}^{2}}$ will be $Rs.3690$.

Note: Here, we have converted the unit into metre, but if a student converts it into centimeter than the length becomes, $length\ \left( l \right)=30\ m+\ 75\ cm=3000+75=3075\ cm$ and due to that the area becomes, $\text{Area of carpet}=3075\times 80=246000\ c{{m}^{2}}$ . and after that to find the cost of carpet students have to again convert area into metre as the cost is given as $Rs.150$ per square meter and the final answer will remain same i.e. $Rs.3690$ per $24.6\ {{m}^{2}}$ . So, students can solve in this way also but the method becomes quite lengthier.