Question

*A survey of 50 students was conducted in a school. They were asked to choose one of the favourite sports between Kabaddi and Football. It was found that 26 students like Kabaddi and 33 students like Football. Each of the student like at least one of the two games. Then find the number of students who like both the sports.*

1️⃣ 8
2️⃣ 7
3️⃣ 9
4️⃣ 10​

Answer 1

There are 50 students, but 10 don’t play either sport, so 40 play either football, hockey or both (50–10=40). From the 40 players, 35 play football, so five play hockey only (40–35=5). Similarly, from the 40 players, 25 play hockey, so 15 play football only (40–25=15). So from the 40 players, 5 play hockey only, and 15 play football only, so 20 must play both sports. (40–5–15=20).

Let’s check and see if it all adds up: 10 students play neither sport, 5 students play only hockey, 15 students play only football, 20 students play both football and hockey. Total 10+5+15+20=50 students. Everyone is accounted for. In addition, 5 students play only hockey, and 20 play both sports, makes 25 hockey players (5+20=25). 15 students play only football, and 20 play both sports, makes 35 football players (15+20=35).

Answer 2

The number of students who like both sports is 9.

Given:

Total students = 50

Number of students who like kabaddi = 26

Number of students who like football = 33

To find: Number of students who like both sports

Solution:

Let set of students who like kabaddi = K ⇒ n(K) = 26

Let set of students who like football = F ⇒ n(F) = 33

⇒ Set of total students = (K∪F) ⇒ n(K∪F) = 50

⇒ Set of students who like both kabaddi and football = (K∩F)

We know that

n(KUF) = n(K) + n(F) - n(K∩F)

⇒ 50 = 26 + 33 - n(K∩F)

⇒ n(K∩F) = 59 - 50 = 9

∴ The number of students who like both sports is 9.

SPJ2