Question

1. In a class of 345 students, the students who took English, Math and
Science are equal in number. There are 30 students who took both
English and Math only, 26 who took both Math and Science only, 28
who took Science and English only and 14 who took all the 3 subjects.
There are 43 students who didn't take any of the subjects. What
percent of students did not take Science? Plz explain how you got the answer briefly.​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

☆ Total number of students in a class = 345

↝ Number of students who didn't take any of Math, English and Science as a subject = 43

So, it means,

↝ Number of students opted atleast Maths or Science or English as subject = 345 - 43 = 302.

↝ Let assume that total number of students who took Maths be x.

↝ Since, it is given that, the students who took English, Math and Science are equal in number.

It means,

↝ Number of students who took Science = x

and

↝ Number of students who took English = x

Now, using venn diagram attached in attachment, we have

↝ Number of Students take all 3 subjects = 14

$\rm :\longmapsto\:g = 14$

↝ Number of students who took English and Math as subject only = 30

$\rm :\longmapsto\:e = 30$

↝ Number of students who took both Math and Science as subject only = 26

$\rm :\longmapsto\:f = 26$

↝ Number of students who took Science and English as subject only = 28

$\rm :\longmapsto\:d = 28$

Now,

Students who took English only a = x - d - g - e = x - 72

Students who took Maths only = b = x - e - g - f = x - 70

Students who took Science only = c = x - d - g - f = x - 68

Now,

According to statement,

Number of students opted atleast one of the subject = 302

$\rm :\longmapsto\:a + b + c + d + e + f + g = 302$

$\rm :\longmapsto\:x - 72 + x - 70 + x - 68 + 28 + 14 + 30 + 26 = 302$

$\rm :\longmapsto\:3x - 210 + 98 = 302$

$\rm :\longmapsto\:3x - 112 = 302$

$\rm :\longmapsto\:3x = 302 + 112$

$\rm :\longmapsto\:3x = 414$

$\rm :\implies\:x = 138$

Now,

↝ Number of students who didn't take Science as subject = a + e + b = 138 - 72 + 30 + 138 - 70 = 164

↝ So percentage of students who didn't take Science as subject =

$\rm  \:  =  \: \:\dfrac{164}{302} \times 100\%$

$\rm  \:  =  \: \:54.304\% \: approx$