A school has 250 students out of which only 50 like to play football, 47 chess and 40 tennis. 35 students like to play both football and tennis, 33 both chess and tennis, 38 football and chess. If 27 students do not like any of the three sports, find the number of students who like all sports.?

Option 4 : 10

Given:

Total students = 250

Only like football = 50

Only like chess = 47

Only like tennis = 40

Both like football and tennis = 35

Both like chess and tennis = 33

Both like football and chess = 38

Students do not like any of the three sports = 27

Calculation:

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According to the diagram,

A + B + C = p + q + r + e + f + g + h      ----(1)

We have,

x = e + h 

⇒ e = x - h

y = g + h 

⇒ y - g = h

z = f + h 

⇒ z - h = f

Now,

A + B + C = (p + q + r + x - h + y - h + h + 27)

A + B + C = (p + q + r + x + y + z + 27 - 2h)

⇒ 250 = 243 - 2h + 27

⇒ 2h = 270 - 250 = 20

⇒ h = 20/2 = 10

∴ The number of students who like all sports are 10.