arithmetic - a train overtakes two boys who are walking in the same direction in which the train is going at the rate of 4 kmhr and 8 kmhr and passes them completely in 9 and 10 seconds respectively the length of the train is - skillgun

4 km/hr = 4*5/18 = 10/9 m/sec and 8 km/hr = 8*5/18 = 20/9 m/sec.
let the length of the train be x metres and its speed be y m/sec.
then, x/(y -10/9) = 9 and x/(y - 20/9) = 10
.'. 9y - 10 = x and 10(9y - 20) = 9x => 9y - x = 10 and 90y - 9x = 200
on solving, we get : x 100
.'. length of the train is 100 m.