| A student goes to school at the rate of \[2\frac{1}{2}\,\,km/h\] and reaches 6 min late. If he travels at the speed of \[3\,\,km/h\] he is 10 min early. What is the distance to the school? |
A) \[4\,\,km\]
B) \[3\frac{1}{2}\,\,km/h\]
C) \[1\,\,km\]
D) \[3\frac{1}{2}\,\,km\]
Correct Answer: A
Solution :
| Let distance of the school be x km. |
| According to the question, |
| \[\frac{x}{5/2}-\frac{x}{3}=\frac{16}{60}\] |
| \[\Rightarrow \] \[\frac{2x}{5}-\frac{x}{3}=\frac{4}{15}\] |
| \[\Rightarrow \] \[\frac{6x-5x}{15}=\frac{4}{15}\] |
| \[\therefore \] \[x=4\,\,km\] |
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