A train starts moving from X at 5:00 p.m. and moves towards Y with a speed of 55km/hr. Another train starts moving from Y at 7:00 p.m. and moves towards X with a speed of 40km/hr. Both of them meet at 11:00 p.m. at Z. What is the ratio of distances XZ and YZ?

Step 1: Calculate the distance XZ
The train from X starts at 5:00 p.m. and meets the other train at Z at 11:00 p.m.

Time traveled by the first train (t
1
​
)=11:00 p.m.−5:00 p.m.=6 hours
Speed of the first train (s
1
​
)=55km/hr
Distance XZ=s
1
​
×t
1
​
=55×6=330km
Step 2: Calculate the distance YZ
The train from Y starts at 7:00 p.m. and meets the first train at Z at 11:00 p.m.

Time traveled by the second train (t
2
​
)=11:00 p.m.−7:00 p.m.=4 hours
Speed of the second train (s
2
​
)=40km/hr
Distance YZ=s
2
​
×t
2
​
=40×4=160km
Step 3: Find the ratio of XZ and YZ

Ratio=
Distance YZ
Distance XZ
​
=
160
330
​
=
16
33
​

Therefore, the ratio XZ : YZ is 33:16.