UPSC CDS Math Speed, Time and Distance Questions

Let the two trains meet at t hours after 9 p.m. Suppose the average speed of the passenger train is v km/hr.
Distance moved by the passengertrain when the two trains meet=v×(t+3)=540
⇒v=

540

t+3

....(1)
Distance moved by the express train when the two trains meet =(v+15)×t=540
⇒v=

540

t

−15.......(2)
From (1) and (2), we have

540

t+3

=

540

t

−15
⇒

540

t

−

540

t+3

=15
⇒

1620

t(t+3)

=15
⇒t2+3t−108=0
⇒(t+12)(t−9)=0
⇒t=9(t>0)
So, the two trains meet 9 hours after 9 p.m., i.e., at 6 a.m.