Air routes are best taken between those cities where the alternative modes of transport are too time-consuming. The total time Mr. Bajaj can take is 8 days or 192 hours.
Thus, we can try the following sequence:
New York City to London by air
London to Paris by road
Paris to Vienna by road
Vienna to Istanbul by road
Istanbul to Dubai by air
Dubai to Mumbai by ship
Mumbai to Kolkata by rail
Kolkata to Hong Kong by air
Hong Kong to Tokyo by air
Tokyo to San Francisco by air
San Francisco to New York City by air.
Calculating the total time and money for this sequence, we find that he takes 190.5 hours and $7465. Now, if we try to replace any more air routes by an alternative mode of transport, we see that he overshoots his time limit. Thus, the minimum number of air routes that Bajaj will have to take is 6.