Question

It takes four hoous for a 300 km journey, if 60 km is done by train and the rest by car. It takes 10 minutes more, if 100 km is done by train and the rest by car. The ratio of the speed of the car to that the train is?

Answer 1

let the speed of the train and car be x and y resp.
60/x+240/y=4
15y+60x=xy--(1)
now
100/x+200/y=4+1/6
600y+1200x=25xy
24y+48x=xy--(2)
from (1) and (2)
15y+60x=24y+48x
12x=9y
y/x=12/9
y/x=4/3

Answer 2

let speed of car =x
and speed of train = y

a/c to question ,
60/y +240/x =4 ------(1)
again,
100/y +200/x =4 +10/60
100/y + 200/x =25/6 ----------(2)

multiply 25/24 in equation (1)

(60/y )25/24 +25/24(240/x )=4 x 25/24 =25/6

now,
10.25/4y+ 250/x =100/y +200/x
(250-200)/x = (100-250/4)/y
50/x = 150/4y
1/x = 3/4y
y/x =3/4

x/y =4/3