Question

In an examination 50% of the students passed in Maths and 70% of students passed in Science while 10% students failed in both subjects. 300 students passed in at least one subject. Find the total number of students who appeared in the examination, if they took examination in only two subjects

Answer 1

Solution :-

Given -

50 % students passed in Mathematics

70 % students passed in Science

10 % of the total students failed in both subjects and 300 students passed in at least one subject.

Let x be the total number of students.

Total students = 100 %

Passed students = 100 - 10 (failed in both subjects)

= 90

Total passed students in at least one subject = (50 + 70) - 90

120 - 90

= 30 %

So, 30 % of the total students passed in at least in one subject.

⇒ (x*30)/100 = 300

⇒ 30x/100 = 300

⇒ 30x = 300*100

⇒ x = 30000/30

⇒ x = 1000

So, total 1000 students appeared in the examination.

Answer 2

Answer:

total number of students =1000

Step-by-step explanation:

Total students = 100%

M - Mathematics and S - Science

number of fail %

=> n(M intersection S) = 10%

number of pass %

=> n(M intersection S) = 100% - 10%

n(M intersection S) = 90%

pass % :

n(M union S) = (300/x)×100

n (A) = 50% and n (B) = 70%.

Now,

n(M union S) = n(A) + n(B) - n(M intersection S)

$\frac{300}{x} \times 100 = 50 + 70 - 90 \\ 3000 = x(120 - 90) \\ 3000 = 30x \\ x = \frac{3000}{30} \\ x = 1000.$

total number students appeared in examination = 1000.