Question

The cost of \[2\dfrac{1}{2}\] meters of cloth is $Rs.\,78\dfrac{3}{4}$. Find the cost of cloth per metre.

Answer 1

Hint: Here we have the cost of \[2\dfrac{1}{2}\] meters of cloth is $Rs.\,78\dfrac{3}{4}$ and we have to find the cost of per metre cloth. For finding the cost of per metre of cloth we will use the concept of unitary method. Firstly, we will convert the mixed fraction values into proper fractions and then we will proceed for the required result.

Complete answer:
According to the given question, we have the cost of \[2\dfrac{1}{2}\] meters of cloth is $Rs.\,78\dfrac{3}{4}$ and we have to find the cost of per metre cloth.
We will convert \[2\dfrac{1}{2}\] into a proper fraction. So,
\[ \Rightarrow 2\dfrac{1}{2} = \dfrac{5}{2}\]
Now we will convert $78\dfrac{3}{4}$ into the proper fraction. So,
$ \Rightarrow 78\dfrac{3}{4} = \dfrac{{315}}{4}$
Therefore, the cost of $\dfrac{5}{2}$ meters of cloth is $\dfrac{{315}}{4}$
Now, we will find the cost per metre of cloth by dividing the given cost by its given length. so,
$ \Rightarrow \dfrac{{\dfrac{{315}}{4}}}{{\dfrac{5}{2}}}$
We can also write it as
$\dfrac{{315}}{4} \times \dfrac{2}{5}$
On multiplying the numbers we get,
$ \Rightarrow \dfrac{{630}}{{20}}$
On dividing the numbers. We get,
$ \Rightarrow 31.5$
Hence, the cost of per metre of cloth is $Rs.\,31.5$

Note:
These types of questions can be solved using the concept of unitary method. The unitary method is used for solving a problem in which we have to find the value of unit in the given terms, using the value of the given quantities and before solving the problems one must recognize and familiarize with the terms of units and values when using the unitary methods in the given problems.