Question

A train after travelling 150 km meets with an accident and proceeds t `3/5` of its former speed and arrives at its destination 8 hours late. Had the accident occurred 360 km further, it would have reached the destination 4 hours late. What is the total distance travelled by the train?
A. 840 km
B. 960 km
C. 870 km
D. 1100km

Answer 1

Correct Answer - C
Let the total distance to be travelled = x km
Speed of train = v km/h
and time taken = t hr.
`(150)/(v) + (x - 150)/(((3v)/(5))) = (t + 8) " " … (1)`
`(510)/(v) + ( x - 510)/((3)/(5) v) = (t + 4) " " …. (2)`
Eq(2) - Eq(1)
`(510)/(v) - (150)/(v) + (x - 510)/((3)/(5) v) - (x - 150)/((3v)/(5)) = -4`
`(360)/(v) - (360 xx 5)/(3v) = -4 implies v = km//hr.`
`t = (x)/(60)`
Put in eqn (1)
`(150)/(60) + (x - 150)/((3 xx 60)/(5)) = ((x)/(60) + 8)`
`(5)/(2) + (x - 150)/(36) = (x)/(60) + 8`
`(x - 150)/(36) - (x)/(60) = 8 - (5)/(2) = (11)/(2)`
`(10 xx - 1500 - 6x)/(360) = (11)/(2)`
`implies 4x - 1500 = (360 xx 11)/(2) = 1980 implies 4x = 3480`
`x = (3480)/(4)` km = 870 km
Alternative solution

In case 1 , train is delayed by 8 hours as it broke down 360 km before .
In case 2 , train is delayed by 4 hours as it covered 360 km before breaking down unlike case 1 .
So we can say , when 360 km earlier breakdown is delaying train by (8-4) = 4 hours
Thus , in case 2 , as train is delayed by 4 hours , so it covers 360 km more
`therefore `Total distance = `150 + 360 xx 2 = 870` km