Math, asked by pchavan0018, 2 months ago

Revisit
Question #27
On a survey regarding a race conducted among the groups, The "X" group spoke the truth, The "Y"
group lied and The "Z" group told the truth and lied, alternatively in no order. Carla, Michael, and Tim
belong to the different groups among X, Y, and Z, not necessarily in the same order. One of them won
the race. Following are the statements of Carla, Michael, and Tim regarding the race
Carta Tim won the race. Tim always speaks the truth. Tím obstructed me at the last moment,
Tim I hadn't obstructed Carla at the last moment. Michael won the race.
Michaet. Carla won the race. Tim is not a member of the "y" group.
Who won the race?​

Answers

Answered by amitnrw
4

Given :  The "X" group spoke the truth, The "Y" group lied and The "Z" group told the truth and lied, alternatively

the statements of Carla, Michael,

and Tim regarding the race.

Carla: Tim won the race. Tim always speaks the truth. Tim obstructed me at the last moment.

Tim: I hadn't obstructed Carla at the last moment. Michael won the race.

Michael: Carla won the race. Tim is not a member of the "Y" group.

To Find : Michael is a member of which group

Solution:

Assume Michael  is from group X   - Spoke truth

Michael: Carla won the race. Tim is not a member of the "Y" group.

Both above statement True

Carla: Tim won the race. Tim always speaks the truth. Tim obstructed me at the last moment.

Tim won the race. Tim always speaks the truth  must be false as per our assumption.  so Carla belongs to group Y  .  

and Tim did not obstruct Carla at the last moment.

Tim: I hadn't obstructed Carla at the last moment. ( True)

Michael won the race. ( False)        Hence Tim is Z

Assume Michael is from group Y

Michael: Carla won the race. Tim is not a member of the "Y" group.

=> Tim  is a member of the "Y" group.  which is not possible.

Hence  NOT possible

Assume  Michael is from group Z

Michael: Carla won the race. Tim is not a member of the "Y" group.

Case 1 :    Carla won the race  ( True )  and Tim is not a member of the "Y" group ( F)

=> Tim is a member of the "Y"

Tim: I hadn't obstructed Carla at the last moment. Michael won the race.

Tim obstructed Carla at the last moment.

Michael did not win the race.

Carla must be from Group X

Carla: Tim won the race.  ( not possible )

Tim always speaks the truth.  ( not possible )

Tim obstructed me at the last

Hence Not Possible

Case 2 :

Carla won the race  ( False )  and Tim is not a member of the "Y" group ( T)

=> Carla did not won the race

Hence Tim Must be from Group X  and Carla from Y

Tim: I hadn't obstructed Carla at the last moment. Michael won the race. all True

Carla: Tim won the race  . Tim always speaks the truth. (T)  Tim obstructed me at the last  

Hence not possible.

SO FINALLY

Michael  is from group X  

Carla  is from group Y  

Tim is  from group Z

Carla won the race

Tim is not a member of the "Y" group.  ( Tim is  from group Z)

Tim did not won the race.

Tim does not always speaks the truth.

Tim did not obstructed Carla at the last moment.

Michael did not won the race

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