Question 95

# In a ‘keep-fit’ gymnasium class there are 15 females enrolled in a weight-loss programme. They all have been grouped in any one of the five weight-groups W1, W2, W3, W4, or W5. One instructor is assigned to one weight-group only.Sonali, Shalini, Shubhra and Shahira belong to the same weight-group. Sonali and Rupa are in one weight-group, Rupali and Renuka are also in one weight-group. Rupa, Radha, Renuka, Ruchika, and Ritu belong to different weight groups. Somya cannot be with Ritu, and Tara cannot be with Radha. Komal cannot be with Radha, Somya, or Ritu. Shahira is in W1 and Somya is in W4 with Ruchika. Sweta and Jyotika cannot be with Rupali, but are in a weight-group with total membership of four. No weight-group can have more than five or less than one member.Amita, Babita, Chandrika, Deepika and Elina are instructors of weight-groups with membership sizes 5, 4, 3, 2 and 1 respectively. Who is the instructor of Radha?

Solution

According to given conditions, the groups are as follows:

Case 1:

W1 : Sonali, Shalini, Shubhra ,Shahira and Rupa
W4: Somya , Ruchika, Jyotika, sweta
: Renuka, Rupali, Komal
: Ritu and Tara

Case 2:

W1 : Sonali, Shalini, Shubhra ,Shahira and Rupa
W4: Somya , Ruchika
: Renuka, Rupali, Komal
: Ritu, Tara, Jyotika, sweta

Hence, Radha must be alone in a group . Therefore, her trainer is Elina.