[100] Two trains A and B start from Town X and Y going towards Y and X respectively. Towns X and Y are 900

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Two trains A and B start from Town X and Y going towards Y and X respectively. Towns X and Y are 900kms apart and it takes A 9 hours to travel between X and Y. A starts at 6:00 am while B starts at 8:00 am. The ratio of speeds of A and B is 5:4. The trains cross each other at point P and then stay at Y and X respectively. The next day, B starts from X at 6:00 am while A starts from Y at 8:00 am.The trains cross each other at point Q. Find the distance between points P and Q.

110

125

100

150

Explanation:

Speed of A,a=900/9=100 km/hr

Speed of B,b=4/5 * 100 =80 km/hr

On day 1 ,distance travelled by A before B starts=2 * 100=200 km

When B starts moving,the relative speed between A and B ,r=100 + 80 =180 km/hr

When B starts moving,the distance between A and B =900-200=700 km

Thus ,time taken for the 2 trains to meet =700/180=35/9 hours

Location of point P=35/9 * 80 from Y=2800/9 km from Y.

On day 2,distance travelled by B before A starts =2 * 80 =160 km

When B starts moving ,the relative speed between A and B,r=100+80=180 km/hr

When B starts moving ,the distance between A and B=900-160=740 km.

Thus time taken for the 2 trains to meet =740/180 =37/9 hours.

Location of point Q =37/9 * 100 from Y=3700/9 km from Y
Therefore ,distance between P and Q =3700 /9 -2800/9 =100 km.

Additional Questions

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