Question

If $1$ liter of milk costs $Rs.19\dfrac{1}{5}$ , what is the cost of $6\dfrac{1}{4}$ liters of milk?
$A)Rs.820$
$B)Rs.320$
$C)Rs.120$
$D)Rs.220$

Answer 1

Hint: First, we will solve the given question using the conversion method which is the mixed fractions into the proper fractions.
The conversion of the mixed fraction to the proper fraction can be done as $a\dfrac{b}{c} = \dfrac{{(a.c) + b}}{c}$. After that, we can find the required value using this method.

Complete step by step answer:
Since from the given that we have $1$ a liter of milk costs $Rs.19\dfrac{1}{5}$ so that we assume the cost as $c = 19\dfrac{1}{5}$
From the given mixed fraction to the proper fraction method, now we have $c = 19\dfrac{1}{5} \Rightarrow c = \dfrac{{(19 \times 5) + 1}}{5}$
Further solving we get $c = \dfrac{{96}}{5}$
Also, since we asked to find the cost of $6\dfrac{1}{4}$ liters of milk, hence we using the same method of conversion then we get $m = 6\dfrac{1}{4} \Rightarrow \dfrac{{(6 \times 4) + 1}}{4}$ and further solving we get $m = \dfrac{{25}}{4}$ where m is the milk and c is the cost.
Hence to find the cost of $6\dfrac{1}{4}$ liters of milk we will multiply it into the $1$ liter of milk costs $Rs.19\dfrac{1}{5}$.
Thus, we have $c \times m$ is the required cost of $6\dfrac{1}{4}$ liters of milk in rupees.
Now solving we get $c \times m = \dfrac{{96}}{5} \times \dfrac{{25}}{4}$ and by the division operation we get $c \times m = \dfrac{{96}}{5} \times \dfrac{{25}}{4} \Rightarrow 5 \times 24$ (canceled the common terms)
Thus, by the multiplication operation, we get $c \times m = 5 \times 24 \Rightarrow 120$
Therefore, the cost of $6\dfrac{1}{4}$ liters of milk is $Rs.120$

So, the correct answer is “Option C”.

Note:
We used the method of multiplication to find the required cost, which is if the cost of the one liter is $c$ and then the cost of the given $6\dfrac{1}{4}$ liters of milk is $m$ then to find the unknown overall cost we used $c \times m$.
Also, some will multiply the method of the mixed fraction to a proper fraction $a\dfrac{b}{c} \times d\dfrac{e}{f} = (a \times d)(\dfrac{b}{c} \times \dfrac{e}{f})$ but this is a completely wrong method because we are not defined the mixed fractions for the multiplication or division directly.