In a club of 80 members, 10 members play none of the games Tennis, Badminton and Cricket. 30 members play exactly one of these three games and 30 members play exactly two of these games. 45 members play at least one of the games among Tennis and Badminton, whereas 18 members play both Tennis and Badminton. The number of Cricket playing members is:

In a club of 80 members, 10 members play none of the games Tennis, Badminton and Cricket. 30 members play exactly one of these three games and 30 members play exactly two of these games. 45 members play at least one of the games among Tennis and Badminton, whereas 18 members play both Tennis and Badminton. The number of Cricket playing members is: Correct Answer 57

From the given conditions, we can represent the number of members playing the various games as follows:

Because 10 members were not playing any game, we get

a + b + c + d + e + f + g = 80 – 10 = 70      ----(i)

Also, 30 members play exactly one of these three games. So,

a + c + g = 30      ---(ii)

Also, 30 members play exactly two of these games. So,

b + d + f = 30      ---(iii)

On combining the equations (i), (ii), and (ii), we get:

e = 70 – (30 + 30) = 10      ----(iv)

While, 45 members play at least one of the games among Tennis and Badminton. So,

a + b + c + d + e + f = 45      ----(v)

Also, 18 members play both Tennis and Badminton. Hence, we get:

b + e = 18      ----(vi)

From equation (iv), we get:

b = 18 – 10 = 8      ----(vii)

Also, substituting the value of b into equation (iii), we get:

d + f = 30 – 8 = 22      ----(viii)

Also, on combining the equations (i) and (v), we get:

g = 70 – 45 = 25      ----(ix)

Hence, we obtain the total number of cricket playing members as:

d + e + f + g = 22 + 10 + 25 = 57

∴  The number of Cricket playing members is 57