Question

If 0.6% of a number is 15, find the number.

Answer 1

Hint: 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 15 to get the required answer.

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 15.
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’ = $\dfrac{{0.6}}{{100}} \times x$ ………..(1)
Now, it is given to be equal to 15.
$ \Rightarrow \dfrac{{0.6}}{{100}} \times x = 15$
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 = 15$
Combining the numerators and the denominators of the left hand side by multiplying them, we will then obtain the following expression:-
$ \Rightarrow \dfrac{{6x}}{{1000}} = 15$
Taking the 100 from division in the left hand side of the above expression to multiplication in the right hand side, we will then obtain the following expression:-
$ \Rightarrow 6x = 15 \times 1000$
Simplifying the calculation in the right hand side of the above expression, we will then obtain:-
$ \Rightarrow 6x = 15000$
Taking the 6 from division in the left hand side of the above expression to multiplication in the right hand side, we will then obtain the following expression:-
$ \Rightarrow x = \dfrac{{15000}}{6}$
Simplifying the calculation in the right hand side of the above expression, we will then obtain:-
$ \Rightarrow x = 2500$
$\therefore $ the original number was 2500 whose 0.6% is 15.

Hence, the answer is 2500.

Note: The students must 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 above we divided 0.6 by 100 and then multiplied it to the original number to get 15.
The students must know that Percentage and Percent are two different terms: Percentage is the quantity obtained by multiplying a quantity by percent. Like in the above question: 0.6 percent of 2500 is 15 and the 15 is the percentage here.