In a class, there are 100 students. They are asked to vote for the teachers they like among five teachers namely Vanita Sehgal, Rashmi Ojha, Dharmendra Kumar, Satish M and L Maraditya. Any student can vote for any number of teachers but they have to vote for at least one. Below is the number of votes achieved by the five teachers. Vanita Sehgal: 47, Rashmi Ojha: 15, Dharmendra Kumar: 41, Satish M: 28, L Maraditya: 25 Determine the least number of students who have voted for a minimum of two of the five teachers.
In a class, there are 100 students. They are asked to vote for the teachers they like among five teachers namely Vanita Sehgal, Rashmi Ojha, Dharmendra Kumar, Satish M and L Maraditya. Any student can vote for any number of teachers but they have to vote for at least one. Below is the number of votes achieved by the five teachers. Vanita Sehgal: 47, Rashmi Ojha: 15, Dharmendra Kumar: 41, Satish M: 28, L Maraditya: 25 Determine the least number of students who have voted for a minimum of two of the five teachers.
The correct option is B 14
X= I + II + III + IV + V = 100
S= I + 2II + 3III + 4IV +5V = 47 + 15 + 41 + 28 + 25 = 156 (each circle added)
S-X= 56= II +2III+3IV+4V
To minimize (II+III+IV+V), we have to maximize 1
To do this make II, III and IV=0
Thus, 4V= 56 ⇒ V= 14
Thus minimum of (II+III+IV+V)= 14
14
X= I + II + III + IV + V = 100
S= I + 2II + 3III + 4IV +5V = 47 + 15 + 41 + 28 + 25 = 156 (each circle added)
S-X= 56= II +2III+3IV+4V
To minimize (II+III+IV+V), we have to maximize 1
To do this make II, III and IV=0
Thus, 4V= 56 ⇒ V= 14
Thus minimum of (II+III+IV+V)= 14
