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  1. A train met with an accident 3 hours after starting, which detains it for one hour, after which it proceeds at 75% of its original speed. It arrives at the destination 4 hours late. Had the accident taken place 150 km further along the railway line,
    the train would have arrived only 3
    1
    hours late.
    2
    Find the length of the trip and the original speed of the train.
    1. 1100 km ; 100 kmph
    2. 1200 km ; 100 kmph
    3. 1200 km ; 90 kmph
    4. 1600 km ; 90 kmph
Correct Option: B

Let A be the starting point, B the terminus. C and D are points where accidents take place.

∴ 0.75 =
3
4

By travelling a 3/4 of its original speed, the train would take 4/3 of its usual time i.e., 1/3 more of the usual time.
∴  1/3 of the usual time taken to travel the distance CB.
= 4 – 1 = 3 hrs.     ...(i)
and 1/3 of the usual time taken to travel the distance
DB = 3
1
− 1 = 2
1
hrs.   ...(ii)
22

Subtracting equation (ii) from (i)
we can write,
1/3 of the usual time taken to travel the distance
CD = 3 − 2
1
=
1
hr.
22

∴  Usual time taken to travel
CD (150 km) =
1
2
1
3

=
3
hr.
2

Usual speed of the train
=
3
= 9 hrs.
1
3

Total time = 3 + 9 = 12 hrs.
∴  Length of the trip = 12 × 100 = 1200 km.


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