| A train P starts from Mokama at 5:00 pm and reaches Hazipur at 6:00 pm. An another train Q starts from Hazipur at 5:00 pm and reaches Mokama at 6:30 pm. At what time, two trains will cross each other? |
A) 5 : 36 pm
B) 4 : 36 pm
C) 6 : 00 pm
D) 7 : 00 pm
Correct Answer: A
Solution :
| Let the distance between Mokama and Hazlpur be x km. |
| Time taken by train P to cover \[x\,\,km=1\,\,h\] |
| Time taken by Q to cover \[x\,\,km=\frac{3}{2}h\] |
| \[\therefore \]Speed of train \[P=x\,\,km/h\] |
| Speed of train Q \[=\left( \frac{2x}{3} \right)km/h\] |
| Let they cross each other y h after 5:00 pm. |
| Then, \[xy+\frac{2xy}{3}=x\] |
| \[\Rightarrow \]\[y+\frac{2y}{3}=1\]\[\Rightarrow \]\[y\,\,\left( 1+\frac{2}{3} \right)=1\] |
| \[\Rightarrow \]\[y=\frac{3}{5}h=\frac{3}{5}\times 60=3\times 12=36\min \] |
| Hence, the two trains meet 36 min after 5:00 pm. |
| \[\therefore \]Meeting time = 5: 36 pm |
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