| A moving train, 66 m long, overtakes another train of 88 m long, moving in the same direction in 0.168 min. If the second train is moving at 30 km/h, at what speed is the first train moving? [SSC (CPO) 2013] |
A) 85 km/h
B) 55 km/h
C) 50 km/h
D) 25 km/h
Correct Answer: A
Solution :
| Suppose the speed of first train \[=x\,\,\text{m}/\min .\] |
| Speed of second train = 30 km/h |
| \[=\frac{30\times 1000}{60}=500\,\text{m}/\min \] |
| Then, relative speed \[=(x-500)\text{m}/\min \] |
| According to the question, |
| \[\text{Time}\,\,\text{taken}=\frac{\text{Sum}\,\,\text{of}\,\,\text{lengths}\,\,\text{of}\,\,\text{train}}{\text{Relative}\,\,\text{speed}}\] |
| \[0.168=\frac{66+88}{x-500}\] |
| \[\Rightarrow \]\[0.168x-84=66+88\] |
| \[\Rightarrow \]\[0.168x=154+84=238\] |
| \[\Rightarrow \] \[x=\frac{238}{0.168}\text{m}/\min =\frac{238}{0.168}\times \frac{3}{50}\text{km/h}\] |
| \[\Rightarrow \] \[x=85km/h\] |
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