Question

In a school $18\%$ of students play tennis and $32\%$ play football. If $432$ actually play tennis, how many students
(i). Are there in school
(ii). Play football

Answer 1

Hint: For solving these types of questions we have the number of students playing tennis and the percentage of them in the total number of students. So we need to use them and find the total number of students in the school. And then using this and the percentage of the number of students playing football we need to obtain the number of students playing football.

Complete step-by-step solution
Given in the question that $18\%$ of students out of total strength play tennis. The actual number of students playing tennis is given as $432$.
Let us assume the total strength of the school is $x$.
Then we can say that \[18\% \text{ of x is } 432\].
That can be mathematically given as $\dfrac{18}{100}\times x=432$
From this, we can get the value of $x$.
It will be $x = 432\times \dfrac{100}{18}$
By performing calculations we will get the number of total students present in the school that is $x = 2400$.
(i). The number of students present in the school is $2400$.
(ii)Here in the question, we are also asked to find the number of students playing football.
It is given in the question that $32\%$ of total students play football.
This implies that the number of football players present in the school are \[32\%\text{ }of\text{ }2400.\]
This can be mathematically written as $\dfrac{32}{100}\times 2400$
By performing the calculations it will be $768$.
We can conclude that the number of students playing football at school is $768$.

Note: While solving these types of questions we should notice the percentage is given for the total number of students or a partial number of students. If by mistake we take the second case as given for the remaining students then we will end up having a completely wrong conclusion.