A) \[40\,h\]
B) \[30\,h\]
C) \[180\,h\]
D) \[120\,h\]
Correct Answer: D
Solution :
Sol. [d] Given. Total distance \[=360\,km\] |
and, Speed of Sumeet\[=\text{12km}/\text{h}\] |
Number of hours taken by Sumeet to complete 1 round |
\[=\frac{\text{Distance}}{Speed}=\frac{360}{12}=30\,h\] |
and, speed of John\[=\text{15 km}/\text{h}\] |
Number of hours taken by John to complete 1 round |
\[=\frac{\text{Distance}}{Speed}=\frac{360}{15}=24\,h\] |
Thus, Sumeet and John complete 1 round in 30 h and 24 h, respectively. |
Now, to find required hours, we find the LCM of 30 and 24 |
\[30=2\times 3\times 5\] |
\[24=2\times 2\times 2\times 3\] |
Then, \[LCM\,\,(30,24)=2\times 2\times 2\times 3\times 5=120\] |
Hence, Sumeet and John will meet each other again after 120 h. |
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