Question

$25\%$ of $600$ is equal to $15\%$ of what number ?

Answer 1

Hint: A percentage is a number or ratio expressed as a fraction of $100\%$. We have to find out how much $25\%$ of $600$. Then assume the unknown number to be $x$. And then equate the value we got by calculating $25\%$ of $600$ to $15\%$ of $x$. Even though we do not know $x$ , we just have to find out how much $15\%$ of it would be. It would definitely be in terms of $x$. And then we solve the equation we get after equating to find the value of $x$.

Complete step by step solution:
For example, we have a number. Let us name it $a$ .
So when we are asked, what is $10\%$ of $a$?
It is nothing but $\dfrac{10}{100}\times a=\dfrac{a}{10}$.
So when I add $10$$\dfrac{a}{10}s$, I would get a complete. $a$
In the same way, $25\%$ of $600$ would be the following :
$\Rightarrow \dfrac{25}{100}\times 600=150$.
Let us assume that our unknown number is $x$.
Now let us find out $15\%$ of $x$ in the same way as we found out $25\%$ of $600$.
It would be the following :
$\Rightarrow \dfrac{15}{100}\times x=\dfrac{3x}{20}$
Now let us equate $25\%$ of $600$ to $15\%$ of $x$i.e $150$ to $\dfrac{3x}{20}$as it is already mentioned in the question that they are equal.
Upon doing so, we get the following :
$\Rightarrow \dfrac{3x}{20}=150$
Let us divide with $3$ on both sides of the equation.
Upon doing so we get the following :
$\begin{align}
  & \Rightarrow \dfrac{3x}{20}=150 \\
 & \Rightarrow \dfrac{x}{20}=50 \\
\end{align}$
Now, let us multiply with $20$ on both sides of the equation.
Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow \dfrac{3x}{20}=150 \\
 & \Rightarrow \dfrac{x}{20}=50 \\
 & \Rightarrow x=1000 \\
\end{align}$
The unknown number $x$ is $1000$.
$\therefore $ Hence, $25\%$ of $600$ is equal to $15\%$ of $1000$.

Note: We should very careful while doing calculations as it may lead to wrong results. Percentage is a very important chapter. It can be clubbed with other concepts and be given as questions. We should be attentive while reading the question. To save time during the exam, we can just do these kind of calculations in our mind. But this needs to heavy practice.