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?
Given:
- Total number of students = 65
- Medals awarded in Hockey = 42
- Medals awarded 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 × 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 × 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.