# [Aptitude] Venn Diagram question from Reader

Question from Ashutosh

In a school of 500 students 20% do not play football 10% do not play cricket and 4% neither play football nor cricket.

1. find out how many play football but not cricket?
2. How many students play both the games?

Since question talks about percentages, first convert them into absolute values

 Percentage Absolute value Total students (U) 100% 500 Don’t play football 20% 1/5th of 500=100 Don’t play cricket 10% 50 Neither football nor cricket (n) 4% 20

In above diagram,
Find the overlapping

## Don’t play cricket ONLY

=  don’t play cricket Minus green color area
=50-20
=30

## Don’t play football only

=don’t play football Minus green area
=100-20
=80

Update the diagram

## Q1. Find out how many play football but not cricket

Ask yourself, what does the orange portion represent?
Those who donot play cricket only.
=those who play football but not cricket
=30.

Answer : 30 students play football but not cricket.

## Q2: How many students play both the games?

Do the sum of all numbers inside the colored circles
=30+20+80
=130

It means there are 130 students who donot play one or more games.
But consider the white area outside those colored circles. What does it represent?
It represents the students who’re not in these circles.
Means the white area outside those circle, represents those students who play both games, because such student cannot be classified in orange, green or blue circle

## Total students in the school

=orange + green + blue + white
500=30+20+80+white
White=500-130=370

It Means, 370 students play both games.

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### अब तक 7 कमेंट्स लिखी गयी

1. ashutosh says:

IN your solution orange shows do not play cricket,blue shows donot play football and green shows donot play both but how we get how many play football but not cricket.if 100 donot plays football including 20 that dont play either this means 400 plays football and similarly we can get 450 plays cricket so students that play football but not cricket should be 50. plz correct me

2. Mrunal ♣ मृणाल ♣ મૃણાલ says:

The "white" area outside those three colored circles = those who play both the games, right?
so if there is a student, who plays football but doesn't play cricket, where can we put him?
we can not put him in white, we cannot put him in blue, we cannot put him in green.
he can be put in the orange portion only.

Therefore, orange portion represents : Those who donot play cricket only. = those who play football but don't play cricket.
and our first question is: find out how many play football but not cricket?

3. vijay bharwani says:

Well try.
But I think u should choose some affirmative question.
Like in the above question,out of 500 students, 100play football,50 play cricket and 20 both.
I think this makes the question easy to understand.

Thanks.

4. मनु झा says:

Mrunal i have a diff opinion on this question.

Q1 . Hoe many play foot ball but not cricket.
Soln. total = 500.if its given in this question that x no. of players dont play foot ball , that also CAN imply that others must hav been playing.(white area ??)
Hence, total who play foot ball = 500 – 100 = 400. (total – who don play fb)
now out hof these who don play cricket = (500-100) – 30 = (total – who dont play cricket=30 , we cant take 50 because the 20 have already been added)

Q2. u have taken the approach of the white area now but not in the Q1 .

5. love says:

thankyou

6. abhi says:

plz solve percentage change graphics

7. Mudasir says:

Msir, Finally i got it after teasing my brains .