Ramesh travels 760km to his home …

Let the speed of train be x kmph and car be y kmph
Condition(i):
Given that Ram travelled a distance of 760 km
Distance travelled by train = 160 km
Recall, time taken = distance / speed
Hence time taken to travel by train = 160/x
Distance travelled by car = 600 km
Time taken to travel by car = 600/y
Total time taken = 8 hours
⇒ 160/x + 600/y = 8 .......... (i)
Condition (ii):
Distance travelled by train = 240 m
Time taken to travel by train = 240 / x
Distance travelled by car = 760 - 240 = 520 km
Time taken to travell by car = 520 / y
Total time taken = 8 hrs + 12 minutes
                         = 8 + (12/60)
                         = 8.2 hours
⇒ 240/x + 520/y = 8.2 ........ (2)
Put 1/x = a and 1/y = b
Hence equations (1) and (2) becomes
160a + 600 b = 8
⇒ 20a + 75b = 1 ........ (3)
240a + 520 b = 8.2
⇒ 120a + 260b = 4.1
⇒ 1200 a + 2600b = 41 ......... (4)
Solving (3) and (4), we get
1900 b = 19
⇒ b = 1/100
⇒ 1/y = 1/100
⇒ y = 100
Put y = 100 in (1), we get
160/x + 600/100 = 8
⇒ 600/x = 8 - 6 = 2
⇒ x = 300
Thus speed of train is 300 kmph and speed of car is 100 kmph.