| Two stations, A and B are 827 km apart from each other. One train starts from station A at 5 am and travel towards station B at 62 km/h. Another train starts from station B at 7 am and travel towards station A at 59 km/h. At what time will they meet? [SBI (PO) Phase I 2015] |
A) 1 : 00 pm
B) 11 : 45 am
C) 12 : 48 : 35 pm
D) 11 : 30 : 30 am
E) 1 : 37 : 45 pm
Correct Answer: C
Solution :
| Let the trains meet after x h of 5 am. |
| So, time taken by train B is \[(x-2)\,h.\] |
| Speed of train A = 62 km/h |
| Speed of train B = 59 km/h |
| Total distance covered = 827 km |
| According to the question, |
| \[62x+59\,(x-2)=827\] |
| \[\Rightarrow \]\[62x+59x-118=827\] |
| \[\Rightarrow \] \[121x=827+118\] |
| \[\Rightarrow \] \[121x=945\] |
| \[\Rightarrow \] \[x=\frac{945}{121}=7\,h\,48\min \,35\,s\] |
| Thus, the trains will meet after 7 h 48 min 35 s of 5 am i.e. at 12: 48: 35 pm. |
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