Question

The cost at $\dfrac{3}{5}$ kg ghee is ${\text{Rs. 96}}$,$\dfrac{5}{2}$ find the cost of:
a.1kg ghee
b.$\dfrac{5}{2}$ kg ghee

Answer 1

Hint: In the given question, you need to first find the cost of 1 kg of ghee which can be easily calculated by using the unitary method. In this method, all you need is to multiply 96 by the reciprocal of $\dfrac{3}{5}$. Once you have obtained this value, the cost of a kg of ghee can be obtained by multiplying the obtained cost of 1 kg by $\dfrac{5}{2}$.

Complete step by step answer:

a.
Let us begin by considering what is given to us. It is given in the question that the cost at $\dfrac{3}{5}$ kg ghee is ${\text{Rs. 96}}$. Thus, we can easily find the cost of 1 kg ghee by the application of the unitary method as follows;
$
  \dfrac{3}{5}{\text{ kg ghee}} \to {\text{Rs. }}96 \\
   \Rightarrow 1{\text{ kg ghee}} \to {\text{Rs. }}96 \times \dfrac{5}{3} \\
   \Rightarrow 1{\text{ kg ghee}} \to {\text{Rs. }}32 \times 5 \\
   \Rightarrow 1{\text{ kg ghee}} \to {\text{Rs. }}160 \\
 $

Thus, we have calculated that the cost of 1 kg of ghee is ${\text{Rs. }}160$.

b.
Now, we are required to find the cost of $\dfrac{5}{2}$ kg ghee. As we already have calculated the cost of 1kg of ghee. Thus, in order to find the value of $\dfrac{5}{2}$ kg ghee all we need to do is multiply the cost of 1 kg of ghee by $\dfrac{5}{2}$.
$
  1{\text{ kg ghee}} \to {\text{Rs. 160}} \\
   \Rightarrow \dfrac{5}{2}{\text{ kg ghee}} \to {\text{Rs. 1}}60 \times \dfrac{5}{2} \\
   \Rightarrow \dfrac{5}{2}{\text{ kg ghee}} \to {\text{Rs. 80}} \times 5 \\
   \Rightarrow \dfrac{5}{2}{\text{ kg ghee}} \to {\text{Rs. 40}}0 \\
 $

Thus, we have calculated that the cost of $\dfrac{5}{2}$ kg of ghee is ${\text{Rs. 400}}$.


Note:: Students must learn properly how to use the unitary method as this method finds its extensive use not only in the theory but practically as well ranging from the distance, time problems to the problems related to calculating the cost of our day to day requirements. Also, make sure to multiply by the reciprocal of $\dfrac{3}{5}$ and not by $\dfrac{3}{5}$ while calculating the cost of 1 kg of ghee as all the further calculations would be based on this step.