Question

The average mark of boys in an examination is 68 and that of girls is 89.If the average mark of all candidates in that examination is 80.Find the ratio of the number of boys to the number of girls that appeared in the examinations

Answer 1

x= boys, y=girls

68x+89y =80 (x+y)

68x + 89y = 80x + 80y

12x = 9y

x/y = 9/12

x:y = 3:4

Answer 2

Answer:

The ratio of the number of boys to the number of girls that appeared in the examinations is 3 : 4

Step-by-step explanation:

Let the number of boys be ' b ' and

The number of girls be ' g '

Given,

The average mark of boys in an examination is 68 ,

Average = Sum of marks of boys / Total number of boys

68 = Sum of marks of boys / b

So,

Sum of marks of boys = 68 b

Similarly for girls it is given,

The average mark of girls is 89 ,

Average = Sum of marks of girls / Total number of girls

89 = Sum of marks of girls / g

So,

Sum of marks of girls = 89 g

Now according to question,

The average mark of all candidates in that examination is 80

Total number of student = Number of boys + Number of Girls

Total number of students = b + g

Also,

The total marks scored will be = Marks scored by boys + Marks stored by girls

Total marks = 68 b + 89 g

Average = Total marks of all students / Total number of students

Substituting the values,

80 =  $\frac{68b+89g}{b+g}$

80b + 80g = 68b + 89g

80b - 68b = 89g - 80g

12b = 9g

So,

$\frac{b}{g}$ = $\frac{9}{12}$

$\frac{b}{g}$ = $\frac{3}{4}$ , that is,

b : g = 3 : 4

Hence,

The ratio of the number of boys to the number of girls that appeared in the examinations is 3 : 4