In a class of 108 students studying maths, english or both; boys and girls are in the ratio of 5: 4. the number of boys studying only maths is 80% of the girls studying only maths and the number of boys studying only english is twice that of the girls studying only english. the total number of boys studying maths is half of the total number of boys in the class. number of girls studying only english is 60% of the girls studying only maths. what is the number of students studying both maths and english?
Answers
Let us say there are 5x boys and 4x girls
so 5x+ 4x= 108
x = 12 so total boys = 5x = 60 total girls = 4x = 48
Let's say girls studying only maths = y
so boys studying only Maths = 0.8y
girls studing only English = z
so boys studying only English = 2z
Number of boys studying both subject =
total boys - ( boys studying maths only + English only )
60 - 0.8y -2z
total boys studying maths = boys studying maths only + boys studying both
= 0.8y + 60 - 0.8y -2z
= 60-2z
According to question this is equal to half of their number in the class
So 60 - 2z = 60/2
=> z = 15
girls studying only English = z which is 60 % of girls studying only maths
Z= 60% of y
15 = 0.6 y
=> y = 25
Girls studying both subject =
total girls - studying maths only - studying english only
48 - 25 - 15 = 8
Boys studying both subject =
total boys - studying maths only - studying english only
60 - 0.8 y - 2z
60 - 0.8 * 25 - 2*15
60 - 20 - 30 = 10
Number of students studying both subject =
girls studying both + boys studying both = 8 + 10 = 18
Answer = 18