Question

The cost of \[7\dfrac{2}{3}m\]of rope is Rs. \[12\dfrac{3}{4}\]. Find its cost per meter.

Answer 1

Hint: In this question first of all we convert both the mixed fraction into improper fraction. Now to find its cost per meter we will use the concept of direct proportional i.e. length of rope is directly proportional to cost of rope.

Complete step-by-step answer:
First convert the mixed fraction into improper fraction.
That is \[7\dfrac{2}{3}m = \dfrac{{\left( {3 \times 7} \right) + 2}}{3}\]m
\[ \Rightarrow 7\dfrac{2}{3}m = \dfrac{{23}}{3}\]m
Similarly,
\[12\dfrac{3}{4} = \dfrac{{\left( {4 \times 12} \right) + 3}}{4}\]
\[ \Rightarrow Rs.12\dfrac{3}{4} = Rs.\dfrac{{51}}{4}\]
We have given cost of \[\dfrac{{23}}{3}\]m of rope is Rs. \[\dfrac{{51}}{4}\]
So, using the concept of direct proportional
The cost of 1 meter rope can be calculated as follows:
\[ \Rightarrow \dfrac{{1 \times \dfrac{{51}}{4}}}{{\dfrac{{23}}{3}}}\]
\[ \Rightarrow \dfrac{{1 \times 51 \times 3}}{{4 \times 23}}\]
\[ \Rightarrow Rs.\dfrac{{153}}{{92}}\]
\[ \Rightarrow \]The cost of rope per meter is\[Rs.\dfrac{{153}}{{92}}\].

Note: Direct proportional: ‘Direct proportional is the relation between two variables when their ratio is equal to a constant value.’
This type of question can be asked with different values.
In general if we have given cost of x meter of rope is Rs.y then its cost per meter is given as below
Cost of x meter rope is Rs. y
\[\therefore \]Cost of 1 meter rope is ?
\[ \Rightarrow \dfrac{y}{x}\] is the cost of rope per meter.