Question

The cost at $\dfrac{3}{5}{\text{kg}}$ ghee is ${\text{Rs}}{\text{.96}}$ , find the cost of i) $1{\text{kg}}$ ghee ii) $\dfrac{5}{2}{\text{kg}}$ ghee.

Answer 1

Hint: The cost of $\dfrac{3}{5}{\text{kg}}$ ghee is given. The cost of $1{\text{kg}}$ ghee and $\dfrac{5}{2}{\text{kg}}$ can be calculated, by simple multiplication. By cross multiplying the $\dfrac{3}{5}{\text{kg}}$ of ghee to the cost of $\dfrac{3}{5}{\text{kg}}$ ghee, we will get the cost of 1kg ghee.

Complete step-by-step answer:
The given values in the question are,
The cost of $\dfrac{3}{5}{\text{kg}}$ ghee is ${\text{Rs}}{\text{.96}}$
from given,
$ \Rightarrow \dfrac{3}{5}{\text{kg}}\,{\text{of}}\,{\text{ghee}} = {\text{Rs}}{\text{.96}}$
i) $1{\text{kg}}$ of ghee will be,
By doing cross multiplication in the above equation we get,
$ \Rightarrow 1{\text{kg}}\,{\text{of}}\,{\text{ghee}} = 96 \times \dfrac{5}{3}$
By solving the above we get,
$1{\text{kg}}\,{\text{of}}\,{\text{ghee}} = 32 \times 5$
By doing multiplication we get,
$\therefore {\text{The cost of }}1{\text{kg}}\,{\text{of}}\,{\text{ghee}} = {\text{Rs}}.160$
ii) $\dfrac{5}{2}{\text{kg}}$ of ghee will be,
Let ${\text{x}}$ be the cost of $\dfrac{5}{2}{\text{kg of}}\,{\text{ghee}}$ ,
$1{\text{kg}}\,{\text{of}}\,{\text{ghee}} = 160$
Then $\dfrac{5}{2}{\text{kg}}\,{\text{of}}\,{\text{ghee}}$ will be,
$\dfrac{5}{2}{\text{kg}}\,{\text{of}}\,{\text{ghee}} = {\text{x}}$
The cost of $\dfrac{5}{2}{\text{kg of}}\,{\text{ghee}}$, ${\text{x}} = $ the cost of $1{\text{kg}}\,{\text{of}}\,{\text{ghee}} \times \dfrac{5}{2}$
By substituting the value, we get,
${\text{x}} = 160 \times \dfrac{5}{2}$
By solving we get,
${\text{x}} = 80 \times 5$
The cost of $\dfrac{5}{2}{\text{kg}}\,{\text{of}}\,{\text{ghee}}$ is,
${\text{x}} = {\text{Rs}}.400$
$\therefore {\text{The}}\,{\text{cost}}\,{\text{of}}\,\dfrac{5}{2}{\text{kg}}\,{\text{of}}\,{\text{ghee}} = {\text{Rs}}{\text{.400}}$
Therefore, the cost of $1{\text{kg}}\,{\text{of}}\,{\text{ghee}}$ is ${\text{Rs}}{\text{.160}}$ and the cost of $\dfrac{5}{2}{\text{kg}}\,{\text{of}}\,{\text{ghee}}$ is ${\text{Rs}}{\text{.400}}$.
Hence, i) the cost of $1{\text{kg}}\,{\text{of}}\,{\text{ghee}}$ is ${\text{Rs}}{\text{.160}}$ and
             ii) the cost of $\dfrac{5}{2}{\text{kg}}\,{\text{of}}\,{\text{ghee}}$ is ${\text{Rs}}{\text{.400}}$.

Note: When the quantity of the material increases and the cost of the material also increases. When the quantity of the material decreases and the cost of the material also decreases. They are directly proportional to each other. So that we are cross multiplying in the above question.
The question ii) can also be solved from the given by doing cross multiplication. The cost of the required quantity is equal to the product of that quantity and the cost of one kilogram. If they are inversely proportional, then we have to solve according to it.