**Problem 1:** An express train traveled at an avg speed of 100km/h stopping for 3 min after 75km. A local train travel at a speed of 50km/h stopping for 1 min after every 25km. If the train began traveling at the same time, how many km did the local train travel in the time it took the express train to travel 600 km?

Solution:

Express train——->600km——->100m/s

stopping for 3 min after 75km

7*3=21

Total time =6hours 21min

Local train —–>50km/h

stopping for 1 min after 25km

In 6hours it travels 300km i.e 6*50=300

including stopages in 6h 12min it covers 300km

21-12=9

now we have to find in 9 min how many km it will travel

60min———>50km

9 min———->?

total distance traveled by local train is 300+7.5=307.5km

**Problem 2:** A, B, C start from Delhi at 10 AM, 11 AM, 12 AM towards Goa and their speed are 3 km/h, 4 km/h, 5 km/h and after meeting on the way, B sends back A to C with a message at what time C will get the message?

Solution:

At 2 PM both A and B will meet

L.C/M OF 3 and 4 is 12

C travels 10 km

12-10=2km

Total time=2:15pm

**Problem 3:** A train left station A form station B at a certain speed after traveling for 100km the train meets with an accident and could travel at th of the original speed and reaches 45 min late at the station B. Had the accident taken place 50km further on it would have reached 30min late at station B. What is the distance between station A and station B?

Solution:

usual new

S 5 : 4

T 4 : 5

4-5=1

After traveling 100km train meet with an accident and reaches 45min late

1——–>

4———->?h

Had the accident taken place 50km further on it would have reached 30min late

1———>

4———->?h

Time gap=3h-2h=1hr

in one hour it travels 50km

1 h———>50km

3*1———->50*3 km

3h————>150km

total distance=100+150=250

Shortcut:

45min-30min=15min

3*50km=15min*3

150km——->45min

100+150=250km