The following common explanation, we get “None is true”.
Hence, option E is correct.
Final table:
Common Explanation
References:
Xagar is travelling to Bihar on 13th of the month.
Only Kushal is travelling to Haryana.
Rajesh is travelling to Assam.
Sanjay and Umesh are travelling in the same state, but not travelling to either Goa or Bihar.
Neither Prem nor Wifaq is travelling to Bihar.
Neither Prem nor Wifaq is travelling to the same city as Rajesh.
Wifaq does not travel to Punjab.
Umesh and Mahid are travelling on the same date, but none of them is travelling to Assam.
Inferences:
From above statements,
Only Kushal is travelling to Haryana. Here, No other person is travelling to Haryana.
Sanjay and Umesh are travelling in the same state and Sanjay & Umesh are not travelling to either Goa or Bihar.
Rajesh is travelling to Assam. Given, neither Prem nor Wifaq is travelling to the same city as Rajesh. Therefore both Prem and Wifaq are not travelling to Assam and also they are not travelling to Bihar which is given in the statement.
Wifaq does not travel to Punjab.
Umesh and Mahid are travelling on the same date and they are not travelling to Assam.
Now, if we observe Umesh, he is not travelling to Goa, Bihar & Assam. No other one is travelling to Haryana except Kushal. Then, Umesh must travel to Punjab (only possibility). Therefore Sanjay also travels to Punjab (Note: Sanjay and Umesh are travelling in the same state)
Similarly, if we observe Wifaq, he is not travelling to Assam, Bihar and Punjab. No other one is travelling to Haryana except Kushal. Then, Wifaq must travel to Goa (only possibility)
All the above information is directly given; by using this we get the initial table as follows,
References:
Sanjay is travelling on neither 11th nor 13th of the month.
Umesh and Xagar are travelling on the same date.
Umesh and Mahid are travelling on the same date.
Kushal and Sanjay does not travel on the same date.
Kushal and Zyva are travelling on the same date.
No one is travelling to Assam and Punjab on 11th of the month.
Only four persons are travelling on 13th of the month.
Inferences:
From above statements,
Sanjay is travelling on 17th of the month (not travelled on 11th and 13th)
Umesh is travelling on 13th of the month (Xagar travelled on 13th)
Mahid is travelling on 13th of the month (Umesh travelled on 13th)
Sanjay is travelling on 17th of the month. Then, Kushal and Zyva not travelled on 17th.
We know Xagar is travelling on 13th of the month. Thus, Umesh, Mahid and Xagar are travelling on 13th.
Kushal and Zyva are travelling on the same date. If Kushal and Zyva travelled on 13th of the month, then totally 5 people travelling on 13th of the month which is not possible (Maximum is 4).
Therefore, Kushal and Zyva are travelling on 11th of the month.
No one is travelling to Assam and Punjab on 11th of the month. Here, Kushal and Zyva are not travelling to Assam and Punjab.
By using above information, we get the following table as shown below,
References:
Only four persons are travelling on 13th of the month.
Only three persons are travelling on 11th of the month.
Wifaq and Prem are travelling on the same date.
At least one person is travelling to Goa on each date.
Not more than three persons are travelling in the same state.
Prem and Rajesh are travelling on the different date.
No one is travelling to Assam and Punjab on 11th of the month.
Inferences:
From above statements,
Out of 10 persons, 4 of them travelling on 13th of the month (given), 3 of them travelling on 11th of the month (given) and then remaining 3 should travel on 17th of the month.
Wifaq and Prem are travelling on the same date. If we observe the table, the only possibility is, Wifaq and Prem should travel on 17th of the month as per above condition.
At least one person is travelling to Goa on each date. Maximum 3 persons can go to the same state. Then each date one person is going to Goa.
We know, Wifaq going to Goa on 17th and then no one going to Goa on 17th of the month. Thus, Prem (17th) is not going to Goa and also Prem is not travelling to Assam and Bihar. No other one is travelling to Haryana except Kushal. Therefore, Prem is travelling to Punjab.
Prem (17th) and Rajesh are travelling on the different date. The one who is travelling to Assam is not travel on 11th. Therefore Rajesh is travelling to Assam on 13th of the month.
Finally, Tarun is travelling on 11th of the month.
By using above information, we get the following table as shown below,
References:
At least one person is travelling to Goa on each date.
No one is travelling to Assam and Punjab on 11th of the month.
Mahid and Zyva do not travel to the same state.
Only two persons are travelling to Bihar, but none of them is travelling on 17th of the month.
Inferences:
From above statements,
At least one person is travelling to Goa on each date. Therefore Mahid is travelling to Goa on 13th.
Tarun is travelling on 11th of the month but not to Punjab as per condition.
Mahid and Zyva do not travel to the same state. Mahid travels to Goa, and then Zyva not travelled to Goa. Therefore, Zyva is travelling to Bihar (only possibility) and finally Tarun is travelling to Goa.
Thus we get the completed table as shown below,