Question

At a school fair, \[70\% \] of the people are under 16 years old. One-third of the people remaining are teachers. If there are 21 teachers at the fair, how many people are there at the fair total?

Answer 1

Hint: Here in this question, we have to find the total number of people in the school fair. To solve this, let us take a number of people in the fair at x and further simplify by using the percentage method and by basic arithmetic operation we get the required solution.

Complete step-by-step answer:
Now, consider the question:
Given,
In school fair,\[70\% \] of the people are under 16 years old
In the fair \[{\dfrac{1}{3}^{rd}}\] of people and the remaining are teachers, there are 21 teachers in the fair.
We have to find the total number of people in the fair including teachers.
Let us take \[x\] be a number of people at the fair.
In \[x\] number of people \[70\% = \dfrac{{70}}{{100}}\] are under 16 years old, then
\[ \Rightarrow x \times \dfrac{{70}}{{100}}\]
On simplification, we get
\[ \Rightarrow \dfrac{{7x}}{{10}}\] people are under 16 years old.
The number of people except under 16 years old are
\[ \Rightarrow x - \dfrac{{7x}}{{10}}\]
Take 10 as LCM, then we have
\[ \Rightarrow \dfrac{{10x - 7x}}{{10}}\]
On simplification, we get
\[ \Rightarrow \dfrac{{3x}}{{10}}\]
Number of teachers at the fair are one-third of remaining, hence, number of teachers at the fair are
\[ \Rightarrow \dfrac{1}{3} \times \dfrac{{3x}}{{10}}\]
On cancelling the like terms, we get
\[ \Rightarrow \dfrac{x}{{10}}\]
But given number of teachers at fair are 21, then
\[ \Rightarrow \dfrac{x}{{10}} = 21\]
Multiply both side by 10, then we get
\[ \Rightarrow x = 21 \times 10\]
\[ \Rightarrow x = 210\]
Hence, there are 210 people at the fair.
So, the correct answer is “210”.

Note: These types of questions are asked in the various Government exams in the quantitative aptitude section. To solve this, first take the unknown value as x it will helps to make solution easy and we have to know, how to write the percentage term in fraction i.e., \[x\% = \dfrac{x}{{100}}\], and know the using of the arithmetic operation like addition, subtraction, multiplication and division.