Question

In a class of 180 students the number of students who passed in mathematics but not in chemistry is less than the total number students who passed in chemistry, and exactly 10 students failed in both the subjects. What is the number of students who passed only in mathematics?

Answer 1

(Correction: There is an error in the question. It is supposed to be "..but not in chemistry is 30 less than..")

We have,

Total number of students = 180

No. of students who failed in both subjects = 10

That leaves us with (180-10) students = 170 students who passed in either of the subjects.

Now, let us consider the no. students who passed in mathematics but not in chemistry to be $x$

Then, the no. of students who passed in chemistry = $x+30$

So, the final equation will be;

$x + x + 30 = 170$

⇒ $2x = 170 - 30$

⇒ $2x = 140$

⇒ $x = 70$

Ans) The number of students who passed only in mathematics = 70

Answer 2

Given:

total students = 180

no. of students failed = 10

no. of students passed in mathematic only < no. of students passed in chemistry

To Find:

no. of students passed in mathematics only =?

Solution:

now, let us assume that,

the no. of students passed in mathematics only = a

the no. of students passed in chemistry only = c

the no. of students passed in chemistry and mathematics both = b

the no. of students failed = d = 10

since, it is given total (a+b+c+d) students = 180

thus putting value of d = 10

we get

a+b+c = 170    ---------(1)

Now, from the given info that,

no. of students passed in mathematic only < no. of students passed in chemistry

we can form equation as

a < b+c

now, adding 'a' on both sides

2a < b+c+a

now putting values from equation 1

a  < 85

thus, the number of students who passed only in mathematics is less than 85