Question

Find the whole quantity if: $12\% $ of it is $Rs.1080$.

Answer 1

Hint: Let the whole quantity be $Rs.x$.
We are basically given that $12\% $ of the whole quantity $Rs.x$ is $Rs.1080$.
So, we will make an equation using this information and then, we will simplify it to find the value of $x$.

Complete step by step solution:
We are given that $12\% $ of the whole quantity is $Rs.1080$.
Let the whole quantity be $Rs.x$.
Then, according to the question, we are given that:
$12\% $ of the whole quantity $Rs.x$ is $Rs.1080$.
The phrase “$12\% $ of the whole quantity $Rs.x$” means that we need to multiply $12\% $ with $Rs.x$, that is, it means $12\% \times Rs.x$.
Thus, the phrase “$12\% $ of the whole quantity $Rs.x$ is $Rs.1080$” yields us an equation $12\% \times Rs.x = Rs.1080$.
Now, we need to solve the equation $12\% \times Rs.x = Rs.1080$.
We know that if we remove the percentage sign from $12\% $, then, we must put $100$ in the denominator, that is, we will get $\dfrac{{12}}{{100}}$ after removing the percentage.
So, now the equation $12\% \times Rs.x = Rs.1080$ becomes:
$\dfrac{{12}}{{100}} \times Rs.x = Rs.1080$.
Now, taking $100$ on the right-hand side of the above equation, we get that:
$12 \times Rs.x = Rs.1080 \times 100$.
This is because on the left-hand side, the number $100$ was with operation division and when we took it on the right-hand side of the equation, the operation with $100$ will be the inverse operation of division, that is, multiplication.
Now, taking $12$ on the right-hand side of the above equation, we get that:
$Rs.x = Rs.1080 \times \dfrac{{100}}{{12}}$.
This is because on the left-hand side, the number $12$ was with operation multiplication and when we took it on the right-hand side of the equation, the operation with $12$ will be the inverse operation of multiplication, that is, division.
Now, multiply $Rs.1080$ with $100$ to get the following equation:
$Rs.x = \dfrac{{Rs.108000}}{{12}}$.
Now, dividing $108000$ by $12$ to get the following equation:
$Rs.x = Rs.9000$.
Thus, the value of $x$ is $9000$.
Therefore, the whole quantity is $Rs.9000$.

Note:
We cannot multiply a percentage with any number until we convert it into a simple number by dividing it by $100$. Always perform algebraic operations one by one to avoid any calculation mistake in the question.