KVPY SA Exam 2012 Question Paper

First train from Pune to Mumbai takes 4hrs.
Second train from Mumbai to Pune takes 3.5hrs.
Speed of train from Pune to Mumbai is V1=

d

4

Speed of train from Mumbai to Pune is V2=

d

3.5

Distance traveled by first train till 9:30 is x=

d

4

×2=

d

2

Say now both trains meet after time from 9:30

x

d∕4

=

d 2 −x

d 3.5

⇒

4x

d

=

3.5

2

−

3.5x

d

⇒

7.5x

d

=

3.5

2

⇒15x=3.5d⇒30x=7d
time taken by first train from 9: 30 is

4x

d

=4(

7

30

) =

14

15

= 56 min
Then both train meet at 9.30 + 56 min = 10 : 26 am