We have already seen in the explanation for previous question, a sequence of routes which
takes 190.5 hours and $\$$7465. To get a cheaper sequence, we will have to replace an expensive
route with a cheaper route, without over shooting the time limit. Possible routes are by ship
from Hong kong to Tokyo, or by rail from San Francisco to New York City. Butt to fit either of
these routes in the sequence, we will have to replace some other non-air routes by air routes.
The best non-air routes to replace are those where the corresponding air routes take much less
time and do not cost as much as air routes between other cities, i.e. Dubai to Mumbai and
Mumbai to Kolkata.
Therefore, if Balaji travels by air from New York City to London, by road from london to Paris to
Vienna to Istanbul, by air from Istanbul to Dubai to Mumbai to Kolkata to Hong Kong to Tokyo
to San Francisco, and by rail from San Francisco to New York City, then he will take 171 hours
and $\$$7225.
The other possible sequence (by ship instead of air from Hong Kong to Tokyo and by air instead
of rail from San Francisco to New York City) tales 177.5 hours and $\$$7265. Therefore, the
minimum total travel fare possible is $\$$7225.