Question

The cost of $2\dfrac{3}{4}metres$ of cloth is $Rs.583$. Find the cost of the cloth per metre.

Answer 1

Hint:Unitary method can be used to calculate the required solution. It will work on simple logic that the lesser the length of cloth, the lesser will be its price. The cost of the cloth per metre can be calculated by dividing the price of the cloth by its length in metre.


Complete step-by-step answer:
It is given that the cost of $2\dfrac{3}{4}metres$ of cloth is $Rs.583$. We are asked to find the cost of the cloth per metre.
Unitary method can be used here to simplify the given statements into mathematical form and further apply the appropriate steps to find the solution.
Unitary method is a technique for solving a problem by initially finding the value of a single unit( here, metre). Since it is given that.
Cost of $2\dfrac{3}{4}metres$ of cloth$ = Rs.583$
Cost of $\dfrac{{11}}{4}metres$ of cloth$ = Rs.583$
We know that the lesser the length of the cloth bought, the cheaper its cost will be.
So, cost of $1metre$ of cloth $ = \dfrac{{583}}{{\dfrac{{11}}{4}}} = \dfrac{{583 \times 4}}{{11}}$
Hence, cost of $1metre$ of cloth$ = Rs.212$
So, the cost of the cloth per metre$ = Rs.212$ per metre.

Note:The student should be familiar with unitary method and some basic logics. For example, if one man takes two days to complete a task, two men will complete the same task in one day. The statement should be read carefully while writing them into mathematical form.Since, we have calculated the cost of the cloth per metre, we can now calculate the cost of any length of that cloth
Total cost$ = $cost per metre$ \times $length needed