Question

Find the value of:
$\begin{align}
  & (i)\text{ }5{\%}\text{ of Rs350} \\
 & \text{(ii) 12}\dfrac{1}{2}{\%}\text{ of 80kg} \\
\end{align}$

Answer 1

Hint:Take the output value $Rs350$ and $80kg$ as $100\%$ . Consider the unknown value as $x$ . Now make a simple equation and find the value of $x$ to get required output.

Complete step-by-step answer:
$(i)$ In this question we need to find the percentage solution. We have been given the output value as $Rs.350$ . Let us represent the unknown value with the help of variable $x$ .
Now let us take $Rs.350$ as $100{\%}$ . Similarly let us take $x$ as $5{\%}$ .
Thus we have, $350=100{\%}$ and $x=5{\%}$ .
Let us make a simple equation out of three two expressions.
Hence we can say that,
$\dfrac{350}{x}=\dfrac{100{\%}}{5{\%}}$ i.e. $\dfrac{350}{x}=\dfrac{100}{5}$ .
Now let us multiply the above expression. Simplify it to get the value of $x$ .
$\Rightarrow x=\dfrac{350\times 5}{100}=\dfrac{1750}{100}=17.5$ .
Thus we got $x=17.5$ .
$\therefore 5{\%}$ of $Rs.350$ is $Rs17.5.$
$(ii)$ We have been given the output value as $80kg$ .Let us represent the unknown value as $x$ .
We can write $12\dfrac{1}{2}$ as, $\dfrac{\left( 12\times 2 \right)+1}{\text{2}}=\dfrac{\text{25}}{\text{2}}.$
Thus, $12\dfrac{1}{2}{\%}=\dfrac{25}{2}{\%}$ .
Now, Let us take $80kg$ as $100{\%}$ . Similarly let us take $x$ as $\dfrac{25}{2}{\%}$ .
\[\begin{align}
  & \therefore 80kg=100{\%} \\
 & x=\dfrac{25}{2}{\%} \\
\end{align}\]
Let us make a simple equation from the above expression.
$\dfrac{80}{x}=\dfrac{100{\%}}{\dfrac{25}{2}{\%}}\Rightarrow \dfrac{80}{x}=\dfrac{100}{\dfrac{25}{2}}$ .
Now let us cross multiply the above expression,
$x=\dfrac{\text{80}\times \text{25}}{\text{2}\times \text{100}}=\dfrac{\text{2000}}{\text{200}}=10$ .
Thus we got $x=10kg$ .
$\therefore 12\dfrac{1}{2}{\%}$ of $80kg=10kg$
Thus we got the final answer as,
$\begin{align}
  & (i)\text{ }5{\%}\text{ of Rs350}=Rs17.5 \\
 & (ii)\text{ 12}\dfrac{1}{2}{\%}\text{ of }80kg=10kg \\
\end{align}$

Note: We can find the percentage solution by a simpler method.
$\begin{align}
  & 5{\%}\times 350=\left( \dfrac{5}{100} \right)\times 350=\dfrac{\text{5}\times \text{350}}{\text{100}}=\dfrac{\text{1750}}{\text{100}}=17.5. \\
 & i.e.\text{ }5{\%}\text{ of }Rs350=Rs17.5 \\
\end{align}$
Similarly,
$12\dfrac{1}{2}{\%}$ of $80kg=\dfrac{25}{2}{\%}$ of $80kg$
$=\dfrac{25}{200}\times 80=\dfrac{\text{25}\times \text{80}}{\text{200}}=10kg.$