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In a "keep-fit" gymnasium class there are fifteen females enrolled in a weight-loss program. They all have been grouped in any one of the five weight-groups $\text{W1, W2, W3, W4, or W5.}$ 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 $\text{W1}$ and Somya is in $\text{W4}$ 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?

  1. Babita
  2. Elina
  3. Chandrika
  4. Deepika
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Ans should be 2) Elina 

There are fifteen females enrolled in a weight-loss program. They all have been grouped in any one of the five weight-groups W1, W2, W3, W4, or W5.

now from given information we can find out the instructor of each group ..  

1.

Sonali, Shalini, Shubhra, and Shahira belong to the same weight-group. Sonali and Rupa are in one weight-group 

From this information we can say "Sonali, Shalini, Shubhra, and Shahira, Rupa" are in same group which is of size 5 members. We cannot include more member in this group becoz of

No weight-group can have more than five or less than one member 

and from

Shahira is in W1,

we can say all these 5 are in W1 group whose instructor is "Amita".

2.

Rupa(W1), Radha, Renuka, Ruchika and Ritu belong to different weight-groups and Rupali and Renuka are also in one weight-group

 so we get one one member of each group

  • (Radha ... ),
  • (Renuka, Rupali....  ),
  • (Ruchika.... ),
  • (Ritu ....),
  • (Sonali, Shalini, Shubhra, Shahira, Rupa) - W1 - Amita

Now we have to find out other members of groups which have sizes 4, 3, 2, 1 respectively.

3.

Somya cannot be with Ritu, Somya is in W4 with Ruchika

  So in w4 (Somya, Ruchika,.. ) and given 

Tara cannot be with Radha. Komal cannot be with Radha, Somya, or Ritu ,  

So from this we can say

  • Radha will not be with Komal and Tara  and 
  • Komal cannot be with Ritu and Somya(Somya, Ruchika)

​So Komal must be in (Rupali, Renuka ) group .

Sweta and Jyotika cannot be with Rupali, but are in a weight-group with total membership of four 

So now we get easily 3 member group (Rupali, Renuka, Komal) 

  • (Radha ... ),
  • (Renuka, Rupali, Komal) - Chandrika
  • (Ruchika, Somya, ...), - W4
  • (Ritu ....),
  • (Sonali, Shalini, Shubhra, Shahira, Rupa) - W1 - Amita

Now we have (Sweta, Jyotika) and (Tara). As above mentioned Tara cannot be with Radha. So she has to be either in (Ruchika, Somya ... ) or with (Ritu ...). But as we already made 3 member and 5 member groups, Tara cannot be with (Ruchika,  Somya ...) group and so she will be with Ritu. So (Ritu, Tara... ) will be there.

come to the Sweta and Jyotika they will be in 4 member group so they have choice either in (Ritu, Tara ) or (Ruchika, Somya ...). So it will be either (Ritu. Tara, Sweta, Jyotika) or (Ruchika, Somya, Sweta, Jyotika)

BUT Radha will remain single (1 member group). So, according to  

Amita, Babita, Chandrika, Deepika, and Elina are instructors of weight-groups with membership sizes 5, 4, 3, 2 and 1, respectively . 

Radha has Elina as instructor. 

 

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