Answer

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**Hint:**We are given the cost value of $7\dfrac{2}{3}$m cloth. First, we will convert this mixed fraction into a simple fraction and the mixed fraction of a given amount as well. Then, we will find the cost of the rope per metre by dividing the price cost of the total rope with the total length of the rope.

**Complete step-by-step answer:**We are given the total length of rope which is $7\dfrac{2}{3}$ metre.

The cost of $7\dfrac{2}{3}$m rope is also provided in the given question which is Rs. $12\dfrac{3}{4}$.

We need to find the cost of rope per metre.

Now, we will convert the mixed fractions into a simpler fraction by the formula $a\dfrac{b}{c} = \dfrac{{(a \times c) + b}}{c}$.

The total length of the rope is $7\dfrac{2}{3}$m which can be written as $7\dfrac{2}{3}m = \dfrac{{(7 \times 3) + 2}}{3}m = \dfrac{{23}}{3}m$.

The total cost of the rope is Rs. $12\dfrac{3}{4}$ which can be written as $Rs.12\dfrac{3}{4} = Rs.\dfrac{{\left( {12 \times 4} \right) + 3}}{4} = Rs.\dfrac{{51}}{4}$.

We know that the total cost of a rope is given by the product of the cost of 1 m of rope and the total length of the rope i. e., the total cost of the rope = (cost per metre $ \times $total length) of the rope.

Now, we will put the values in the formula mentioned above. On substituting the values, we get

$\therefore $$\dfrac{{51}}{4}$= cost per metre of the rope $ \times $ $\dfrac{{23}}{3}$

$ \Rightarrow $cost per metre = $\dfrac{{51}}{4} \times \dfrac{3}{{23}} = 1\dfrac{{61}}{{92}} = 1.66$

**Therefore, the cost of one metre rope is Rs. 1.66.**

**Note:**In such problems, you may get confused about the conversion of mixed fractions and also in the formula used. you should also take care of the language you are using in your examination as this is a word problem. This problem can directly be solved by dividing the total cost from the total length.

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