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 tjey meet again

Answer 1

Solution:

Given,

• Circular field has a circumference = 360 km.
• Number of Cyclists = 3
• Their distance travelled in a day= 48 km , 60 km and 72 km.

☞ Number of days taken by First Cyclists to cover distance = 360/48 = 7.5 days

☞ Number of days taken by Second Cyclists to cover distance = 360/60 = 6 days

☞ Number of days taken by Third Cyclists to cover distance = 360/72 = 5 days

Now, It is clear that Minimum duration of time for which they will meet Again together, Will be the LCM of their time taken.

So, LCM of 7.5 , 6 and 5 day is 30 days.

Therefore, They will meet again in 30 days.

Answer 2

$\huge{\mathfrak{\underline{\underline{Solution:}}}}$



Speed of first, second and third cyclist are 48 km/day, 60 km/day and 72 km/day. In terms of km/hr,

48 km/day = $\dfrac{48}{24}$ km/h = 2 km/h

60 km/day = 60 km/24 h

72 km/day = $\dfrac{72}{24}$ km/h = 3 km/h

Time = $\dfrac{Distance}{Speed}$

Time for 1st cyclist = $\dfrac{360}{2}$ = 180 hrs

Time for 2nd cyclist = $\dfrac{360}{\bigg(\dfrac{60}{24}\bigg)}$
Time for 2nd cyclist = 144 hrs

Time for 3rd cyclist = $\dfrac{360}{3}$ = 120 hrs

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

Total Time taken in days = $\dfrac{720}{24}$
Total Time taken in days = = 30 days