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?

Answer 1

First, we will get how much time all three cyclists take to cover a circumference of 360 km 

So, the time taken for cyclist1 = 360/48 = 7.5 days

So, the time taken for cyclist2 = 360/60 = 6 days

So, the time taken for cyclist3 = 360/72  = 5 days

Here, LCM of 7.5, 6, 5 = 30

So, they will meet after 30 days.

Now, in 30 days, first cyclist will travel = 30/7.5 = 4 rounds

In 30 days, second cyclist will travel = 30/6 = 5 rounds

In 30 days, third cyclist will travel = 30/5 = 6 rounds

So, after 30 days, all the 3 cyclists will meet at starting point.

Answer 2

"Time covered by the cyclist to make a round of 360 km is 30 days.

Solution:

Let us take A, B, C are three cyclists.

Time covered by the cyclist $A\quad =\quad \frac { 360 }{ 48 } \quad =\quad 7.5days\quad \Rightarrow \quad 7.5\quad \times \quad 24{ hours }\quad =\quad 180$

Time covered by the cyclist $B\quad =\quad \frac { 360 }{ 60 } \quad =\quad 6{ days }\quad \Rightarrow \quad 6\quad \times \quad 24{ hours }\quad =\quad 144$

Time covered by the cyclist $C\quad =\quad \frac { 360 }{ 72 } \quad =\quad 5days\quad \Rightarrow \quad 5\quad \times \quad 24{ hours }\quad =\quad 120$

L.C.M of 180, 144, 120 = 720 hours

Therefore, it takes 30 days to meet each other."