Question

There are three groups of students in a class, Lotus, Lilly, and Rose. While students belonging to Lotus
do not lie, students belonging to Rose lie on every alternate statement. However, the students of Lilly
group never tell the truth. Ronald, Shelly, and Mike belong to different groups.
When a teacher asked, Ronald said, "Shelly belongs to the Rose group", Shelly refuted Ronald's
statement and said, "Mike belongs to the Rose group". However, Mike said, "Shelly definitely belongs
to the Rose group".​

Answer 1

Answer:

shelly is a member of Lilly group

Answer 2

Given  : students belonging to Lotus do not lie,

students belonging to Rose lie on every alternate statement.  

students of Lilly group never tell the truth.

Statements :

Ronald said, "Shelly belongs to the Rose group",

Shelly  said, "Mike belongs to the Rose group".

Mike said, "Shelly definitely belongs to the Rose group"

To Find : which is correct ?

Shelly is a member of Lilly group

Mike is a member of Lotus group

Ronald belongs to Lotus group

Shelly belongs to Lotus group​

Step-by-step explanation:

Case 1 :  Ronald  always speak Truth  belongs to  Lotus

and Ronald said, "Shelly belongs to the Rose group",  =>

Shellu must belong to rose group

But  Mike also said, "Shelly definitely belongs to the Rose group"   hence mike is speaking truth which is not possible as Mike must be then from Lily group

Case 2 : Shelly always speak Truth  belongs to  Lotus

Shelly  said,  "Mike belongs to the Rose group".  

=> Mike belongs to the Rose group

Mike said, "Shelly definitely belongs to the Rose group" which is a lie and Mike can speak lie  

Ronald said, "Shelly belongs to the Rose group",  a lie  Hence Ronald is from Lily group

Shelly Lotus , Mike Rose and Ronald - Lilly is possible

Case 3 : Mike always speak Truth  belongs to  Lotus

Mike said, "Shelly definitely belongs to the Rose group"

Hence Shelly belongs to the Rose group

Ronald said, "Shelly belongs to the Rose group"  a truth hence Ronald must be from rose group again a  contradiction

so  we get results as

Shelly Lotus ,

Mike Rose

Ronald - Lilly

Shelly belongs to Lotus group​  is correct option

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