Question

# A circular field has a circumference of 360 km. Three cyclists start together and can cycle 48, 60 and 72 km a day, round the field. When will they meet again?

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Solution

## GIVEN: A circular field has a circumference of 360 km. Three cyclists start together and can cycle 48, 60, and 72 km a day, round the field. TO FIND: When they meet again. In order to calculate the time when they meet, we first find out the time taken by each cyclist in covering the distance. Number of days 1st cyclist took to cover 360 km = $\frac{\mathrm{Total}\mathrm{distance}}{\mathrm{Distance}\mathrm{covered}\mathrm{in}1\mathrm{day}}=\frac{360}{48}=7.5=\frac{75}{10}=\frac{15}{2}\mathrm{days}$ Similarly, number of days taken by 2nd cyclist to cover same distance = $\frac{360}{60}=6\mathrm{days}$ Also, number of days taken by 3rd cyclist to cover this distance = $\frac{360}{72}=5\mathrm{days}$ Now, LCM of $\left(\frac{15}{2},6\mathrm{and}5\right)=\frac{\mathrm{LCM}\mathrm{of}\mathrm{numerators}}{\mathrm{HCF} \mathrm{of}\mathrm{denominators}}=\frac{30}{1}=30\mathrm{days}$ Thus, all of them will take 30 days to meet again.

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