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03 Jan 2020, 02:16
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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:
67% (02:48) correct
33%
(02:53)
wrong
based on 242
sessions
History
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Two trains, each 100 meters long take 60 seconds to cross each other if traveling in the same direction and 10 seconds to cross each other when traveling in opposite direction. Find the speed of the faster train.
A. 30 kmph
B. 35 kmph
C. 42 kmph
D. 50 kmph
E. 84 kmph
A. 30 kmph
B. 35 kmph
C. 42 kmph
D. 50 kmph
E. 84 kmph
03 Jan 2020, 02:40
Kudos
Bookmarks
Approach:
- Assume the speed of trains be S1 and S2.
- Total Distance = length of both trains: 100+100 = 200 m
- Time taken T1 = 60 sec, T2 = 10 sec
- S1+S2 = 200/10 => 20 m/s ....1
- S1-S2 = 200/60 => 10/3 m/s ....2
- Add (1)&(2), We get S1 = 35/3 m/s and further S2 = 25/3 m/s
- speed of the faster train(in Kmph) 35/3*18/5 = 42Kmph
Option C
- Assume the speed of trains be S1 and S2.
- Total Distance = length of both trains: 100+100 = 200 m
- Time taken T1 = 60 sec, T2 = 10 sec
- S1+S2 = 200/10 => 20 m/s ....1
- S1-S2 = 200/60 => 10/3 m/s ....2
- Add (1)&(2), We get S1 = 35/3 m/s and further S2 = 25/3 m/s
- speed of the faster train(in Kmph) 35/3*18/5 = 42Kmph
Option C
03 Jan 2020, 11:15
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Bunuel
Let the two speeds be v1 and v2, with v1 > v2.
Same direction: If we treat v2 as stationary, the speed of the faster train is effectively v1 - v2. The faster train needs to travel 200 meters to fully cross the slower train (since each train is 100 meters long). Then \(\frac{200 }{ {v1 - v2}} = 60\) seconds.
Opposite direction: If we treat either stationary, the speed of the other train is effectively v1 + v2. Then \(\frac{200 }{ {v1 + v2}} = 10\) seconds.
So we get \(v1 + v2 = 20\) m/s and \(v1 - v2 = 10/3\) m/s. We can add the equations to get \(2* v1 = 70/3\) m/s and \(v1 = 35/3\) m/s . Finally convert to kmph by multiplying \(\frac{{1 km} }{ {1000 m}}\) and \(\frac{{3600 s} }{ {1 h}}\),
\(\frac{35}{3} * \frac{3600 }{ 1000} = 35 * \frac{1200 }{ 1000} = 35 * \frac{6 }{ 5} = 42\)
Ans: C
