60 boys are living in a hostel and like to play two sports viz. Cricket and Chess. (1/4)th of the boys like to play cricket, (2/3)rd of the remaining like to play chess. If 24 boys do not like to play any of the sport, then how many boys like to play both cricket and chess?
Correct Answer : a ) 9Explanation :
Numbers of boys who play cricket (A) are =60×(1/4)=15
Now, remaining number of boys = 60 – 15 = 45
Numbers of boys who like to play chess (B) are =45×(2/3)=30
According to the question,
Number of boys who do not like to play any of the sports = 24 boys
Therefore, the number of boys who like to play any of the sports will be n(A∪B) = Total number of boys – number of boys who do not to play any of the sports
⇒ 60 – 24 = 36
Thus, from set theory number of boys who do not like to play any of the sports (A∩B) will be given as
⇒ n(A∪B) = n(A) + n(B) - n(A∩B)
36 = 15 + 30 - n(A∩B)
n(A∩B )= 45 - 36 = 9 boys
Hence, (a) is the required solution.
Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2& 3, UPSC CDS, UPSC NDA etc.