Question

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

Answer 1

It is given that 10% students failed in both the subjects then we can say that 90% students passed in at least one or both subjects. But as 300 passed in at least one subject. If the students passed in a subject may have failed in nother subject then 70% + 50% must be equal to 90% but it is not, as some must have passed in both subjects thatis they are,

( 70% + 50% ) - 90% = The students
passed in both
subjects.

120% - 90% = 30%

The percentage of students passed in only one subject is = 90% - 30%
= 60%

The total number ( taken as t ) of students appeared the exam will be ,

$\frac{300}{t} \times 100 = 60$
$\frac{30000}{t} = 60$
$t = \frac{30000}{60}$
$t = 500$
Therefore the total students appeared the exam will be 500