Question

If 35% of a number is 175, then what percent of 175 is that number?

Answer 1

Hint: In this question, we will proceed by considering the required number as \[x\]. Then we will consider 35% of \[x\], and equate it equal to 175 to get \[x\]. Further we will consider the required percent as \[y\]and solve for this value as \[y\% \] of 175 is \[x\]. So, use this concept to reach the solution of the given problem.

Complete step-by-step answer:
Let us consider the required number as \[x\].
We know that \[p\% \] of \[q\] is given as \[\dfrac{{p \times q}}{{100}}\].
We have been given 35% of \[x\] is 175. So, we have
\[
   \Rightarrow \dfrac{{x \times 35}}{{100}} = 175 \\
   \Rightarrow x = \dfrac{{175 \times 100}}{{35}} \\
  \therefore x = 500 \\
\]
We have to find by what percent of 175 is the number \[x = 500\].
Let us consider the required percent as \[y\].
So, we have \[y\% \] of 175 is equal to 500.
\[
   \Rightarrow \dfrac{{y \times 175}}{{100}} = 500 \\
   \Rightarrow 175y = 500 \times 100 \\
  \therefore y = \dfrac{{50000}}{{175}} = 285.714 \\
\]
Therefore, the required percent is 285.714%.

Note:It should be noted that when we talk about percentage, then it is always in 100. Also, we should remember that \[a\] percent of \[b\] is always equal to \[b\] percent of \[a\]. Also, we should make sure that we are not assuming two unknowns by the same variable because it may lead to wrong calculations in case of problems based on percentage.