Question

If $0.6\% $ of a number is $24$, find the number.

Answer 1

Hint: Here, in the given question, we are given that $24$ is $0.6\% $ of a number, and we need to find that number. We will first assume the required number to be some algebraic quantity and then find the $0.6\% $ of it using the required formula and substitute it equal to $24$ to get the required answer.

Complete step by step answer:
Let us assume that the required number is $'x'$. Since, we are given that $0.6\% $ of a number is equal to $24$. We know that $a\% $ of a number means $\dfrac{a}{{100}}$ of that number. Therefore, $0.6\% $ of a number $'x'$ will be equivalent to $\dfrac{{0.6}}{{100}}$ of the number $'x'$.

Here, the word ‘of’ refers to multiplication.
$ \Rightarrow 0.6\% $ of the number $'x'$ = $\dfrac{{0.6}}{{100}}$ of $'x'$
$ \Rightarrow 0.6\% $ of the number $'x'$ = $\dfrac{{0.6}}{{100}} \times x$
Now, it is equal to $24$.
$ \Rightarrow \dfrac{{0.6}}{{100}} \times x = 24$
We can remove the decimal from the numerator of the left hand side by using the fact that $0.6 = \dfrac{6}{{10}}$. Then, we will get:
$ \Rightarrow \dfrac{6}{{10}} \times \dfrac{1}{{100}} \times x = 24$

On multiplication of terms of the LHS, we get
$ \Rightarrow \dfrac{{6x}}{{1000}} = 24$
On cross multiplication of terms, we get
$ \Rightarrow 6x = 24 \times 1000$
Taking the $6$ from multiplication in the LHS of the above expression to division in the RHS, we will then obtain the following expression:
$ \Rightarrow x = \dfrac{{24 \times 1000}}{6}$
On simplification, we get
$ \therefore x = 4000$

Therefore, the original number was $4000$ whose $0.6\% $ is $24$.

Note: Note that percent comes from the Latin word per-centum which means $1$ of $100$, because we calculate the percentage using this fact only. Like in the given question we divided $0.6$ by $100$ and then multiplied it to the original number to get $24$. We should take care of the calculations so as to be sure of our final answer.