 # A school awarded 42 medals in hockey, 18 in basketball and 23 in cricket.

Question:

A school awarded 42 medals in hockey, 18 in basketball and 23 in cricket. if these medals were bagged by a total of 65 students and only 4 students got medals in all the three sports, how many students received medals in exactly two of the three sports?

Solution:

Given:

- Total number of students $=65$

- Medals awarded in Hockey $=42$

- Medals awarded $\mathrm{n}$ Basketball $=18$

- Medals awarded in Cricket $=23$

- 4 students got medals in all the three sports.

To Find:

Number of students who received medals in exactly two of the three sports.

Total number of medals = Medals awarded in Hockey + Medals awarded in Basketball + Medals awarded in Cricket

Total number of medals $=42+28+23$

$=83$

It is given that 4 students got medals in all the three sports.

Therefore, the number of medals received by those 4 students $=4 \times 3=12$

Now, the number of medals received by the rest of 61 students $=83-12=71$

Among these 61 students, everyone at least received 1 medal.

Therefore, the number of extra medals $=71-1 \times 61=10$

Therefore, we can say that 10 students received more than one and less than three

medals, or we can say that 10 students received medals in exactly two of three sports.