Question

In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is.

• A. 22
• B. 33
• C. 10
• D. 45

Answer 1

Answer: (D)

45

Answer 2

$n ( M ) = 55 , n ( P ) = 67 , n ( M \cup P ) = 100$

Now, $n ( M \cup P ) = n ( M ) + n ( P ) - n ( M \cap P )$

$100 = 55 + 67 - n ( M \cap P )$

∴$n ( M \cap P ) = 122 - 100 = 22$

Now n (P only) = $n ( P ) - n ( M \cap P )$ $= 67 - 22 = 45$ .