In a school, 80% of the students play either football or cricket .....

Solution

Given:

• 80% of the students, in a school, play either cricket or football and rest don’t play any sport
• 35% of the students, who play a sport, play only cricket

To find:

• The percentage of students, in the school, who play football

Approach and Working:

• Let us assume that the total number of students in the school = 100x

o So, the number of students, who play cricket or football = 100x * \(\frac{80}{100}\) = 80x
o The number of students, who play only cricket = 80x * \(\frac{35}{100}\) = 28x
o This implies that the number of students, who play football = 80x - 28x = 52x

• Therefore, percentage of students, who play football = \((\frac{52x}{100x}) * 100 = 52\)%

Hence, the correct answer is Option C.

Answer: C

Given: In a school, 80% of the students play either football or cricket, and the rest don’t play any sport.

Asked: If 35% of the students, who play any sport, play only cricket, then what percent of students, in the school, play football?

In a school, 80% of the students play either football or cricket, and the rest (20%) don’t play any sport.

35% of the students, who play any sport (80%), play only cricket = 35% *80% = 28%

Percent of students, in the school, play football = 80% - 28% = 52% (since 80% play football or cricket and 28% play only cricket.)

IMO C

Given:
1. In a school, 80% of the students play either football or cricket, and the rest don’t play any sport.
2. 35% of the students, who play any sport, play only cricket

Asked: What percent of students, in the school, play football?



35%*80% = 28% Play only cricket

Let percent of students playing football = x%

2x - 52 + 80 - x = 80
x = 52%

IMO C

\(n(F∩C) = 80\) , \(n(F∩C)' = 20\) ; \(n(F∪C) = 100\)

\(n(C)\) is 35% of 80 = 28
\(n(F)\) is 80 - 28 = 52

Answer must be (C) 52, its better to solve such problems using Venn Diagram for beginners....

Let’s assume there are 100 students in the school. So 80 of them play either football or cricket, and 0.35 x 80 = 28 students play only cricket. So 80 - 28 = 52 students play football (note: any of these 52 students can play only football or both football and cricket). Therefore, the percent of students who play football is 52/100 = 52%.

Answer: C

Hi all,
Can any of you please explain through a venn diagram?
And can we just do this using percents only and not assuming the total value as 100 or 100X?

This is a fairly easy question on Venn diagrams. Since all the values in the question are given in terms of percentages, let’s assume the total number of students in the school to be 100x.

80 percent of the people play either football or cricket i.e. 80x students are in either the cricket or the football circles. 20 percent i.e. 20x students don’t play any sport.

35% of students who play any sport i.e. 35% of 80x i.e. 28x students play only cricket. Since all the regions of the circles should total to 80x, the remaining 52x students constitute the students who play football.

The Venn diagram looks like the one below



The correct answer option is C.
Hope that helps!

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