A train met with an accident 3 hours after starting, which

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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)
	2		2

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.
	2		2

∴ 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.

the train would have arrived only 3	1	hours late.
	2