Let the total distance traveled by Jay be D km.

As per given data-

Jay travels half journey by train at 40 kmph

∴ He travels D/2 km at 40 kmph SPEED.

∴ Time taken to travel D/2 km = $(\frac{{distance}}{{speed}})$

$({\rm{Time\;taken\;to\;travel\;}}\frac{{\rm{D}}}{2}{\rm{\;km}} = \frac{{\frac{D}{2}}}{{40}})$

⇒ Time taken to travel D/2 km = D/80 hr---- (1)

After travelling D/2 distance half of remaining distance he travels at 20 kmph.

∴ He travels D/4 distance at 20 kmph.

$(\therefore {\rm{Time\;taken\;to\;travel\;D}}/4{\rm{\;km}} = \frac{{distance}}{{speed}})$

Time taken to travel D/4 km $(= \frac{{\frac{D}{4}}}{{20}})$

Time taken to travel D/4 km = D/80 hr---- (2)

& Remaining distance he travels at 2.5 kmph.

∴ He travels D/4 distance at 2.5 kmph.

∴ Time taken to travel D/4 km = $({\rm{}}\frac{{distance}}{{speed}})$

Time taken to travel D/4 km = $(\frac{{\frac{D}{4}}}{{2.5}})$

Time taken to travel D/4 km = D/10 hr---- (3)

By ADDING results (1), (2) & (3) we get total time taken by Jay to travel distance D.

∴ Total time taken by RAJ to travel distance D = (D/80) + (D/80) + (D/10)

As we know,

$(Average\;speed = \frac{{Total\;distance}}{{Total\;time\;taken\;to\;travel}})$

⇒ Average speed = $(\frac{D}{{\frac{D}{{80}} + \frac{D}{{80}} + \frac{D}{{10}}}})$

⇒ Average speed = $(\frac{D}{{\frac{D}{{80}} + \frac{D}{{80}} + \frac{{8D}}{{80}}}})$(By keeping denominators equal)

⇒ Average speed = $(\frac{D}{{\frac{{10D}}{{80}}}})$

⇒ Average speed = 8 kmph.