$\begin{array}{l} \text { If } \mathrm{A} \text { and } \mathrm{B} \text { are subsets of universal set } \mathrm{X} \text { such that } \mathrm{n}(\mathrm{X})=200, \mathrm{n}(\mathrm{A})=90, \mathrm{n}(\mathrm{B})=80 \text { , }\\ n\left(A^{\prime} \cap B^{\prime}\right)=40, \text { then } n\left(A \cap B^{\prime}\right)= \end{array}$

• A

  70
• Correct answer
  B

  80
• C

  20
• D

  10

Solution

$$ \begin{aligned} n\left(A \cap B^{\prime}\right) &=n(A)-n(A \cap B) \\ n(x) &=200 \\ & \sim(A \cap B)=n(A)+n(B)+2\left(A^{\prime} \cap B^{\prime}\right) \\ &-n(X) \\ n\left(A \cap B^{\prime}\right) &=90-10 \\ &=80 \end{aligned} $$

Hence, the correct answer is option: 'B'.