Question

If $$22.5$$ m of cloth costs Rs. 1350. What is the cost of $$6{\displaystyle \frac{3}{4}}$$ m of cloth?

Answer 1

Hint: Here, we will find the price of 1 metre of cloth using the information given in the question. We will find the improper fraction representation of $$6{\displaystyle \frac{3}{4}}$$ .Then we will multiply the improper fraction with the price per metre of the cloth to find cost of $$6{\displaystyle \frac{3}{4}}$$ m of cloth.

Complete step-by-step answer:
We know the cost of 22.5 metres of cloth. We will use the unitary method to find out the cost of $$6{\displaystyle \frac{3}{4}}$$ metres of cloth.
First, we will find the cost of 1 metre of cloth. As 22.5 metres of cloth costs Rs. 1350 dividing 1350 by 22.5 will give us the price of cloth per metre.
Cost of 1 metre cloth $$={\displaystyle \frac{1350}{22.5}}$$
We will remove the decimal in the denominator by multiplying the numerator by 10:
$$\Rightarrow$$ Cost of 1 metre cloth $$={\displaystyle \frac{13500}{225}}$$
Factorizing the numerator and denominator, we get
$$\Rightarrow$$ Cost of 1 metre cloth $$={\displaystyle \frac{60\times 9\times 25}{9\times 25}}$$
We will cancel out the common factors and find the price of 1 metre of cloth. Therefore, we get
$$\Rightarrow$$ Cost of 1 metre cloth $$=60$$
The price of 1 metre of cloth is Rs. 60.
We need to find the price of $$6{\displaystyle \frac{3}{4}}$$ metres of cloth. First, we will convert $$6{\displaystyle \frac{3}{4}}$$ into an improper fraction. We will substitute 6 for $$a$$ , 3 for $$b$$ and 4 for $$c$$ in the formula $${\displaystyle \frac{ac+b}{c}}$$ to convert a mixed fraction into an improper fraction:
$$\begin{array}{l}6{\displaystyle \frac{3}{4}}={\displaystyle \frac{\left(6\times 4\right)+3}{4}}\\ \Rightarrow 6{\displaystyle \frac{3}{4}}={\displaystyle \frac{27}{4}}\end{array}$$
We need to find the price of $${\displaystyle \frac{27}{4}}$$ metres of cloth. We will multiply price of 1 metre of cloth by $${\displaystyle \frac{27}{4}}$$ :
Cost of $${\displaystyle \frac{27}{4}}$$ metre cloth $$={\displaystyle \frac{27}{4}}\times 60$$
Simplifying the terms, we get
$$\Rightarrow$$Cost of $${\displaystyle \frac{27}{4}}$$ metre cloth $$=27\times 15=405$$
$\therefore$ The price of $$6{\displaystyle \frac{3}{4}}$$ metres of cloth is 405 rupees.

Note: We can also find the price by using the formula $${\displaystyle \frac{x\times p}{l}}$$ where $$x$$ is the length of cloth whose price has to be found and $$p$$ is the price of cloth of length $$l$$ :
$$\begin{array}{l}\mathrm{p}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{e}={\displaystyle \frac{{\displaystyle \frac{27}{4}}\times 1350}{22.5}}\\ \Rightarrow \mathrm{p}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{e}=405\end{array}$$

To convert a mixed fraction into an improper fraction, we need to multiply the whole number with the denominator and add the numerator. The result obtained will be the numerator of the required improper fraction and its denominator will be the same as the denominator of the mixed fraction; that is $$a{\displaystyle \frac{b}{c}}$$ is equivalent to the improper fraction $${\displaystyle \frac{ac+b}{c}}$$ .