Question

The cost of $7\dfrac{2}{3}$ meters of cloth is $Rs.12\dfrac{3}{4}$. Find the cost per meter.

Answer 1

Hint: It is given the cost of $7\dfrac{2}{3}$ meters of cloth is $Rs.12\dfrac{3}{4}$, first, we will convert mixed fraction to improper fraction, now to find the cost a one-meter cloth we will divide the cost of the cloth by length of cloth given. After dividing we’ll get the value for the cost of cloth per meter that is asked.

Complete step by step Answer:

Given data: the cost of $7\dfrac{2}{3}$ meters of cloth=$Rs.12\dfrac{3}{4}$
A mixed fraction is a whole number plus a fractional part. An improper fraction is a fraction where the numerator is larger than the denominator and if the numerator is smaller than the denominator then it is called a proper fraction, we can only interchange the improper fraction to mixed fraction and vice versa.
If we have a mixed fraction $a\dfrac{b}{c}$ then its form in improper fraction will be $\dfrac{{ac + b}}{c}$
It is given that the cost of $7\dfrac{2}{3}$ meters of cloth is$Rs.12\dfrac{3}{4}$
So, the cost of one-meter cloth will be equal to the cost of $7\dfrac{2}{3}$ meter cloth divide by $7\dfrac{2}{3}$ meters.
Therefore, the cost of a one-meter cloth$ = \dfrac{{12\dfrac{3}{4}}}{{7\dfrac{2}{3}}}$
On converting into improper fractions we get,
\[ \Rightarrow \] The cost of a one-meter cloth $ = \dfrac{{\dfrac{{51}}{4}}}{{\dfrac{{23}}{3}}}$
By multiplying the numerator and denominator by $\dfrac{3}{{23}}$, we get,
\[ \Rightarrow \] The cost of a one-meter cloth $ = \dfrac{{51}}{4} \times \dfrac{3}{{23}}$
On simplification we get,
\[ \Rightarrow \] The cost of a one-meter cloth $ = \dfrac{{153}}{{92}}$
This is also in the form of improper fraction converting to mixed fraction, we get,
\[ \Rightarrow \] The cost of a one-meter cloth $ = 1\dfrac{{61}}{{92}}$
Therefore, the cost of per meter cloth is $Rs.1\dfrac{{61}}{{92}}$.

Note: Remember to always write the final measurements or units as similar to the measurement or units given in the question, alter it in the final answer only if it is asked in the question. As in this question, we have given the length and the cost in mixed fraction so our final answer i.e. rate, it should also be in mixed fraction.