A, B, C and D are four medical representatives of a company. Each of them must visit exactly two of the eight cities - Delhi, Chennai , Kolkata, Hyderabad, Bangalore, Mumbai, Lucknow and Patna and each city is visited by only one person. C does not visit Mumbai and Delhi, While D does not visit Patna, Kolkata and Hyderabad. B does not visit Lucknow and Patna. Whereas A does not visit Bangalore and Chennai. Patna and Bangalore are visited neither by B nor by C. If Delhi and Lucknow were visited by A, then which one of the following cities could B visit ?

We know that A visits Delhi and Lucknow. So A is done.

Now, we are given the following conditions:

B does not visit Lucknow, Patna

C does not visit Mumbai or Delhi

D does not visit Patna, Kolkata, Hyderabad

A does not visit Bangalore, Chennai (This is already satisfied)

If we notice, Patna and Bangalore are visited neither by B nor by C. So, Patna and Bangalore must be visited by A or D But A already has 2 cities  so both must go to D

Therefore, D visits Bangalore and Patna

Now, remaining cities: Chennai, Kolkata, Hyderabad, Mumbai

These must be divided between B and C (2 each)

C cannot visit Mumbai , so C must pick 2 from: Chennai, Kolkata, Hyderabad. Therefore, B will get the remaining 2 cities

Possible choices for C:

C → Chennai, Kolkata and  B → Hyderabad, Mumbai

C → Chennai, Hyderabad and  B → Kolkata, Mumbai

C → Kolkata, Hyderabad and B → Chennai, Mumbai

In all cases, B always gets Mumbai.