Discussion

Explanation:

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Let the number of people liking

exactly 1 game = a (all orange areas together) = 90
exactly 2 games = b (all green areas together)
all three games = c (blur area)
none of the three games = n

⇒ n + a + b + c = 130   
⇒ n + b + c = 40 ...(1)

To maximise 'n', we need to minimise 'b + c'.

Also, when we add those who like Cricket (60), Football (45) and TT (45), we add 'a' once, 'b' twice and 'c' thrice.
∴ a + 2b + 3c = 60 + 50 + 45
⇒ 2b + 3c = 65   ...(2)

Now, to maximise 'b + c', we should maximise the variable with lesser coefficient and to minimise 'b + c', we should maximise the variable with higher coefficient.

Here, we need to minimise 'b + c', hence we will minimise 'b' and maximise 'c'.
For, 'b' and 'c' to be integers, least value 'b' can take is 1.

Hence, 2 + 3c = 65
⇒ b = 21

∴ Minimium possible value of 'b + c' = 1 + 21 = 22.

⇒ n + b + c = 40
⇒ n + 22 = 40
⇒ n = 18

Hence, option (c).

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