Discussion

Explanation:

The given information can be represented through a Venn Diagram.

The number students training for Cricket is 40 less than those who are not training for Cricket.

Let the number of students training for cricket = x and not training for cricket will be 400 - x.

∴ x + 40 = 400 – x

⇒ x = 180

From the figure we can see that,

Number of people training for only Football and Hockey = 90 – y.

∴ Number of people who train for only Cricket and Football = 120 – (90 - y) = 30 + y.

⇒ Number of people training for Cricket = 180 = 70 + (30 + y) + y

⇒ y = 40

Now, total number of people = 400 = 180 + 2x + (90 - y) + x + 2y

⇒ 130 = 3x + y = 3x + 40

⇒ x = 30

Now, 

Number of students who train in more than one of these sports is 180 = y + 120 + (students training for only Cricket and hockey)

⇒ Students training for only Cricket and Hockey = 60 – y = 20

⇒ Number of students training for Only Cricket = 70 – 20 = 50.

Hence, we get the following diagram.

​​​​​​​

∴ Number of students who do not train for any of the 3 sports = 2y = 80.

Hence, option (a).

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