SOLUTION: in a class 2/10 play cricket, 3/5 play carrom ,5play none, 15 play both games how many students in the class?

1. At the beginning, my reading of this condition was as follows:


      "In a class 2/10 play cricket, 3/5 play carrom; 15 of them play both games; 5 play none.  
      How many students are there in the class?"


   which is natural. (Or seemed to be natural to me).

   OK. Let "x" be the number of students in the class. Then we have this equation for x:

    = .    (1)

   Why "-15" ? Because we counted twice those 15, who play both games, among    and  .

   If so, then from (1)  we have   =   and then   = ,  x = -50.

   So, the solution is  x = -50 students, which is absurd.

   The conclusion is: this reading is incorrect.


2. It means that I should consider another reading of the condition:


      "In a class 2/10 play cricket, 3/5 play carrom; in addition to them, 15 play both games; 5 play none.  
      How many students are there in the class?"


   Under this reading, the equation takes another form:

    = .    (2)

   The solution is x = 100 students,   which may have sense.


This completes my analysis.