Question

On a certain day 25%of the total students of a school were absent .the ratio of the number of boys to the number if girls who were 11:19 the total number of girls enrolled in the school is 3850 the number of boys who were absent is 700 more than that of girls .find total number of students in school

Answer 1

Given :

Total number of girls enrolled in school = 3850

The ratio of number of boys to girls absent = 11 : 19

The percentage of total students absent = 25%

The number of boys absent = 700 + number of girls absent

To Find :

Total number of students in school

Solution :

Let The total number of students in school = N

The number of students absent = 25% of total students

                                                    = 0.25 × N

∵ ratio of boys to girls were absent = 11 : 19

So, Let The number of boys absent = 11 x

And the number of girls absent = 19 x

i.e   11 x + 19 x = 0.25 N

Or  30 x = 0.25 N

i.e       x = $\dfrac{0.25 N}{30}$

So,

The number of boys absent = 11 x = 11 × $\dfrac{0.25 N}{30}$

And the number of girls absent = 19 x = 19  × $\dfrac{0.25 N}{30}$

Again

∵ The number of boys absent = 700 + number of girls absent

i.e  11 × $\dfrac{0.25 N}{30}$ = 700 +  19  × $\dfrac{0.25 N}{30}$

Or,   11 × $\dfrac{0.25 N}{30}$ -  19  × $\dfrac{0.25 N}{30}$ = 700

Or,  $\dfrac{0.25 N}{30}$ × 8 = 700

Or, $\dfrac{0.25 N}{30}$ = $\dfrac{700}{8}$

Or,  N = $\dfrac{700 \times 30}{8 \times 0.25}$

∴  Number = N = 10500

Hence, Total numbers of students in school is 10500  Answer

Answer 2

Step-by-step explanation:

Consider no.of boys present be 11x

and no. of girls present be 19x

and no. of absent student i.e 25% =10x

therefore total student enrolled = 40x

Assumption is required

no. of student absent=10x

no. of girls absent=3x

no. of boys absent=7x

it means

4x= 700

x= 175

similarly

if we take it in girls enrolled= 19x+3x=22x

22x= 3850

x= 175

total no. of student enrolled= 40x

40×175=7000