n a academy of 80 members, each member plays at least one of the two games viz. tennis and cricket. The number of members who play tennis are 50. The number of members who play cricket are also 50. None of the members who plays only tennis knows French. Members who know French and play both these games are 3/7th of the number of members who play only cricket and know French. What is the minimum possible number of members who play both tennis and cricket but do not know French?

A. 6
B. 4
C. 2
D. 8
E. 5

• Using Venn diagram and solving d above puzzle we get,
  No. of players who play only tennis=30
  No. of players who play only cricket=30
  No. of players who play both=20
  Since the players who play only tennis do not know French, people who know French belong to the other group of 50( 30 playing only cricket + 20 playing both ). Let x be the people who know French, y b d cricket players who know French and z b the players playing both who know French. Now, from d given data, we get,
  z=(3/7)*y
  We have,
  y+z=x
  i.e. (7/3z)+z=x or (10*z)/3=x
  10*z should b a whole no. and should b maximum since d number of players playing both who dont know French is to b minimum. Therefore, if z=18, we get x as a whole no. and 20-18, gives 2 as the answer.
  
  
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