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07 May 2026, 08:33
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
69% (02:27) correct
31%
(02:04)
wrong
based on 16
sessions
History
Date
Time
Result
Not Attempted Yet
A train leaves City A for City B at 8:00 AM traveling at a constant speed. Another train leaves City B for City A at 10:00 AM on the same track at a speed 25% faster than the first train. The two cities are 630 km apart. After the trains cross each other, the first train reaches City B exactly 2 hours later than the second train reaches City A. What is the speed of the first train?
(A) 28 km/h
(B) 30 km/h
(C) 31.5 km/h
(D) 35 km/h
(E) 40 km/h
(A) 28 km/h
(B) 30 km/h
(C) 31.5 km/h
(D) 35 km/h
(E) 40 km/h
07 May 2026, 21:29
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Let speed of first train = v
Speed of second train = 1.25v
Distance = 630 km
Let they meet after t hours from 8:00 AM.
First train time = t
Second train time = t − 2
So meeting equation:
vt + 1.25v(t − 2) = 630
vt + 1.25vt − 2.5v = 630
2.25vt − 2.5v = 630
v(2.25t − 2.5) = 630 ...(1)
After meeting:
Remaining distances:
first arrives 2 hours later
So:
(630 − vt)/v − (630 − 1.25v(t − 2))/(1.25v) = 2
Solving simplifies to:
v = 31.5
final answer: 31.5 km/h (C)
Speed of second train = 1.25v
Distance = 630 km
Let they meet after t hours from 8:00 AM.
First train time = t
Second train time = t − 2
So meeting equation:
vt + 1.25v(t − 2) = 630
vt + 1.25vt − 2.5v = 630
2.25vt − 2.5v = 630
v(2.25t − 2.5) = 630 ...(1)
After meeting:
Remaining distances:
- First train remaining time = (630 − vt)/v
- Second train remaining time = (630 − 1.25v(t − 2))/(1.25v)
first arrives 2 hours later
So:
(630 − vt)/v − (630 − 1.25v(t − 2))/(1.25v) = 2
Solving simplifies to:
v = 31.5
final answer: 31.5 km/h (C)
07 May 2026, 21:54
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RahulGowdaK
Ratio of their speeds = 4 : 5
Ratio of time taken = 5 : 4 (since both travel the same distance AB)
This difference of 1 in time is actually 4 hrs (First train started early by 2 hrs and reached late by 2 hrs)
So the multiplier is 4 and hence time taken by first train overall = 5*4 = 20 hrs
Speed of first train = 630 km / 20 hrs = 31.5 km/h
Answer (C)
Ratios discussed here:
Ratios Video: https://youtu.be/5ODENGG5dvc
Time Speed Distance using Ratios: https://youtu.be/7ASEIvxYPCM
