The circumfetence of a field is 360km. Three cyclist run 48km, 60km and 72km a day. When will they meet again
Answers
Circumference of the field (circle)=360 km
For the first cyclist:-
He covers 48 km in a day, so he will cover 360 km in (1/48×360) days
= 7.5 days
=180 hours
For the second cyclist:-
He covers 60 km in a day, so he will cover 360 km (1/60×360) days
= 6 days
=144 hours
For the third cyclist:-
He covers 72 km in a day, so he will cover 360 km in (1/72×360) days
=5 days
=120 hours
Now, the LCM of 180, ,144 and 120 is 30.
So, they all will meet again after 30 days.
Verification:-
In 30 days first cyclist will travel = 30/7.5= 4 rounds
In 30 days 2nd cyclist will travel = 30/6= 5 rounds
In 30 days third cyclist will travel = 30/5 = 6 rounds
So, after 30 days all the three cyclists will meet at start point.
Given,
circumfetence of a field is 360km,
Three cyclist run 48km, 60km and 72km a day.
So the distance covered by the first cyclist every day is = 48 km
The number of days taken by the first cyclist to cover the round = 360/48 = 7.5days
1day ------ 24 hours
7.5 days ----- ?
=7.5×24
=180 hours
The distance covered by the second cyclist in a day = 60 km
The number of days taken by the second cyclist to cover the round = 360/60 = 6 days
1day ---- 24 hours
6 days ---- ?
=6×24
=144 hours
The distance covered by the third cyclists in a day is = 72 km
The number of days taken by the thrid cyclist to cover the round = 360/72 = 5 days
1 day ---- 24 hours
5 days ---- ?
=5×24
=120 hours
Now let us take the L.C.M of 180, 144, 120.
We get LCM = 720 hours
= 720/ 24
= 30 days
So,Therefore When will they meet again is 30 days.