A and B started their journeys from X to Y and Y to X, respectively. After crossing each other, A and B completed remaining parts of their journeys in $6 \frac{1}{8}$ hours and 8 hours, respectively. If the speed of A is 32 km/h, then the speed, in km/h, of B is:

28

Formula used :-

(\(\frac{Speed \;of \;train\; P}{Speed\; of\; train\; Q}\))^2 = \(\frac{After \;meeting \;each \;other\; time \;taken\; by \;train\; Q}{After \;meeting \;each \;other\; time \;taken\; by \;train\; P}\)

6 hours 7.5 minutes = \(\frac{49}{8}\) hours

Let the speed of Y be A  km/hr

(\(\frac{32}{A}\))² = \(\frac{8 × 8}{49 }\)

(\(\frac{32}{A}\))2 = \(\frac{64}{49 }\)

\(\frac{32}{A}\) = \(\frac{8}{7 }\)

A = 32 × \(\frac{7}{8 }\)

A = 28 km/hr

So , The speed of Y is 28 km/hr.