Question

In a school of 1200 students, \[45\% \] are girls, \[30\% \] of girls and \[25\% \] of boys come to school by school bus. What percentage of students use the bus?

Answer 1

Hint: Firstly, find the number of boys and girls in the school. After it, find how many boys and girls come to school using the school bus and then find the total number of students (both boys and girls) who travel to school using the school bus. Thus, by finding the \[\% \] of students using the school bus to travel to school, we will get our answer.

Complete step-by-step answer:
It is given that; there are 1200 students in a school out of which \[45\% \] of students are girls.
$\therefore $ Number of girl students = \[45\% \] of 1200
$ = \dfrac{{45}}{{100}} \times 1200$
 $ = 45 \times 12$
 = 540
Thus, the number of girl students is 540.
So, the number of boy students is the difference of the total number of students and number of girl students.
$\therefore $ Number of boy students = 1200 – 540
  = 660
Now, it is given that \[30\% \] of girl students use the school bus to travel to the school.
So, \[30\% \] of 540 $ = \dfrac{{30}}{{100}} \times 540$
= $3 \times 54$
= 162
So, 162 girl students out of 540, use the school bus to travel to the school.
Also, \[25\% \] of boy students use school buses to travel to school.
So, \[25\% \] of 660 $ = \dfrac{{25}}{{100}} \times 660$
 $ = \dfrac{{660}}{4}$
 = 165
So, 165 boy students out of 660, use school buses to travel to the school.
Thus, 165 + 162 = 327 students out of 1200 students use the school bus to travel to school.
Now, we have to find \[\% \] of students who travel by school bus.
$\therefore $ % of students $ = \dfrac{{327}}{{1200}} \times 100\% $
$ = \dfrac{{327}}{{12}}\% $
 \[ = 27.25\% \]
Thus, \[27.25\% \] of students use school buses to travel to school.

Note: Here, do not directly add the \[\% \] of students travelling through school bus i.e. \[30\% \] girls + \[25\% \] boys = \[55\% \] students travel through school bus.
Here, we firstly have to find the total number of students who travel through the school bus using the information given.
Now, find the \[\% \] of students using the school bus., which eventually gives us the correct answer.