Answer

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**Hint:**To get the percentage of the given quantity in the form of $a\%$ of $b$, we will use the formula $\dfrac{a}{100}\times b$. Then, we will simplify it in the simplest form with the help of proper mathematical operations to get the required answer.

**Complete step by step answer:**

a. $25\%$ of $500$

Since, the formula for getting the percentage of the above given quantity is:

$\Rightarrow \dfrac{a}{100}\times b$

Where, $a=25$ and $b=500$.

Now, we will substitute the respective values of $a$ and $b$in the formula as:

$\Rightarrow \dfrac{25}{100}\times 500$

Here, we will get $12500$ after multiplying $25$ and $500$ from the above step as:

$\Rightarrow \dfrac{12500}{100}$

Using division, we will have:

$\Rightarrow 125$

Hence, the percentage of $25\%$ of $500$ is $125$.

b. $30\%$ of ₹$1200$

We will use the formula for getting the percentage of the above given quantity.

$\Rightarrow \dfrac{a}{100}\times b$

Where, $a=30$ and $b=1200$.

Substitute $30$ for $a$ and $1200$ for $b$in the formula as:

$\Rightarrow \dfrac{30}{100}\times 1200$

After multiplying $30$ and $1200$, we will get $36000$ from the above step as:

$\Rightarrow \dfrac{36000}{100}$

We will have $360$by division from the above step as:

$\Rightarrow 360$

Hence, the required answer is $360$.

c. $45\%$ of $500$ KM

For getting the percentage of the above given quantity, we can use the formula mentioned below:

$\Rightarrow \dfrac{a}{100}\times b$

Where, $a=45$ and $b=500$.

Substituting $30$ for $a$ and $1200$ for $b$ in the above formula as:

$\Rightarrow \dfrac{45}{100}\times 500$

Now, we will multiply $45$ with $500$ and will get $22500$ from the above step as:

$\Rightarrow \dfrac{22500}{100}$

By division, we will have $225$from the above step as:

$\Rightarrow 225$

Hence, the required value of the given quantity is $225$.

**Note:**We can check whether the procedure for obtaining the required value is correct or incorrect in the by using the following formula of getting percent of obtained value.

$=\dfrac{\text{Obtained value}}{\text{Total}}\times 100$

Check for $25\%$ of $500$ -

Since, the obtained value is $125$ and total is $500$. So, from the formula-

$=\dfrac{125}{500}\times 100$

Now, we will do the necessary mathematical calculation:

$\begin{align}

& =\dfrac{125}{5} \\

& =25\% \\

\end{align}$

Hence, the solution is correct.

For $30\%$ of ₹$1200$-

Since, the obtained value is $360$ and the total is $1200$. So, from the formula-

$=\dfrac{360}{1200}\times 100$

Now, we will do the necessary mathematical calculation:

$\begin{align}

& =\dfrac{360}{12} \\

& =30\% \\

\end{align}$

Hence, the solution is correct.

For $45\%$ of $500$ KM

Since, the obtained value is $225$ and the total is $500$. So, from the formula-

$=\dfrac{225}{500}\times 100$

Now, we will do the necessary mathematical calculation:

$\begin{align}

& =\dfrac{225}{5} \\

& =45\% \\

\end{align}$

Hence, the solution is correct.

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