Question

$25$ people for program $A,50$ people for program $B,10$ people for both. So, the number of employees employed only for $A$ is

• A. $15$
• B. $20$
• C. $35$
• D. $40$

Answer 1

The correct option is A

$15$

Explanation for correct option:

Find the number of employees employed only for $A(i.e.,n(A-B\left)\right)$:

Given, Number of elements in set $A,n\left(A\right)=25$

Number of elements in set $B,n\left(B\right)=50$

Number of common elements in set $A$and $B,n(A\cap B)=10$

$\Rightarrow$ $n(A-B)=25-10$ $\mathbf{\because }\mathit{n}\mathbf{(}\mathit{A}\mathbf{-}\mathit{B}\mathbf{)}\mathbf{}\mathbf{=}\mathbf{}\mathit{n}\mathbf{\left(}\mathit{A}\mathbf{\right)}\mathbf{}\mathbf{-}\mathbf{}\mathit{n}\mathbf{(}\mathit{A}\mathbf{\cap }\mathit{B}\mathbf{)}$

$\Rightarrow$ $n(A-B)=15$

$\therefore$The number of employees employed only $A$is $\mathbf{15}$

Hence, Option ‘A’ is Correct.