Question

A circular field has a circumference of 260km. Three cyclists start together and can cycle 60km, 72km, 90km a day, around the field .After how many days will they meet again at a starting point.

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

First cyclist =60 km
Second cyclist = 72 km
Third cyclist = 90 km
All the three cyclist meets at a starting point :

LCM of 60, 72, 90

                 6              60, 72, 90

 

                3            10, 12, 15

                   5           10,  4,  5

                    2           2, 4,  1

                                    1,  2,  1

          LCM = 6x3x5x2x2=360 km

So after 360m run all the three cyclist meet together