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10th Class Mathematics Real Numbers Question Bank MCQs - Real Numbers

  • question_answer
    A circular field has a circumference of\[\text{36}0\text{ km}\]. Two cyclists Sumeet and John start together and can cycle at speeds of \[\text{12 km}/\text{h}\] and \[\text{15 km}/\text{h}\] respectively, round the circular field. They will meet again at the starting point after:

    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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