Read the following information carefully and answer the questions which follow.
Pawan, Rohit, Sanjay, Tushar, Umesh and Vivek are 6 friends who belong to 6 different cities among Allahabad, Hyderabad, Delhi, Lucknow, Guwahati and Bhopal, not necessarily in the same order. During their summer break they decided to visit some other city. Each one of them went to one of the cities from the above list. No two friends visited the same city. Further, the following information is also known
1. Tushar is from Guwahati and Pawan visited Allahabad.
2. Umesh is from Delhi and Sanjay visited Lucknow.
3. Rohit is not from Allahabad and Vivek is not from Hyderabad.
4. Rohit visited Tushar’s hometown and Vivek visited Umesh’s hometown.
5. The person who is from Hyderabad visited Lucknow.
For how many people can their home town and the city they visited be uniquely determined?
Solution
We know that Tushar is from Guwahati and Umesh is from Delhi.
Now Pawan visited Allahabad so, Pawan cannot be from Allahabad. Thus, one among, Rohit, Sanjay and Vivek has to be from Allahabad. However, from 3 we can rule out Rohit. Thus, either Sanjay or Vivek will be from Allahabad. However, from 2 and 5 we can infer that Sanjay is from Hyderabad and visited Lucknow. Thus, Vivek must be from Allahabad. One among Rohit and Pawan will be from Bhopal and the other one will be from Lucknow.
Now we know that Pawan visited Allahabad, Sanjay visited Lucknow, Rohit visited Guwahati and Vivek visited Delhi. Thus one among Tushar and Umesh will visit Hyderabad and the other one will visit Bhopal.
Thus we have the following table
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