Q. 11

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?

Answer :

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.


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RS Aggarwal - Mathematics