Question

In a certain class, one-third of the students were absent. Half of the total strength attended the Maths test and one-fourth of the total strength attended the Physics test. If $6$ students attended both the tests and every student who was present attended at least one of the two tests, then how many students were absent on that day ?

• A. $16$
• B. $18$
• C. $24$
• D. $32$

Answer 1

The correct option is C $24$

$\text{Let the total no. of students are}x\text{.}$

$\text{No. of}\text{students which were absent}=\frac{x}{3}\text{.}$

$\text{No. of students which were present}=\frac{2x}{3}$

Now,

No. of dtudents who gove maths test $=\frac{x}{2}$

No. of students who gave physics test: $\frac{x}{4}$

No. of students who gave both test $=6$

A denotes no. of students whogawe maths test

B denotes no. of students who gave physics test

$n\left(A\right)=\frac{x}{2}n\left(B\right)=\frac{x}{4}n(A\cap B)=6$

$n(A\cup B)=$ no. of students which were present

$\begin{array}{cc}n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)& \\ \frac{2x}{3}=\frac{x}{2}+\frac{x}{4}-6& \\ & x=72\end{array}$

$\text{No. of students which are absent}=\frac{72}{3}=24$