0Question:
A and B are moving in the same direction with speeds 5 and 11 while C is in moving in the opposite direction at speed 3. If they start together, at how many distinct meeting points they should meet ?
Answer:
Oa : 2
Solution : A and B in sane direction while C in opposite.
So, A and B will have 11 - 5 = 6 distinct meeting points.
A and C will have 3 + 5= 8 distinct meeting points.
B and C will have 11 + 3 = 14 distinct meeting points.
A, B and C will have HCF (6, 8, 14) = 2 distinct meeting points.
They will meet at 2 distinct points on the track
Question:
A , B and C run around a circular track of length 1.2 km at speed of 5m/s , 7m/s and 8m/s respectively starting from the same point simultaneously. While A and C run in the same direction, B runs in the opposite direction .
a) When will all of them meet for first time they start the race ?
b) In the first hour of the race how many more times will B and C meet than the number of times A and B meet .
Answer:
Oa : a) 400, b) 9
a) Let us start by figuring out with A and B will meet for the first time. This is given by => (Track length /Relative Speed )
= 1200/12 = 100 seconds
Now think about when A and C meet for the first time. This is given by 1200/3 = 400 seconds.
B and C will meet for the first time after 1200/15 = 80 seconds
A and B will meet once every 100 seconds or at times 100 .seconds from the start.
A and C will meet every 400 seconds or at times 400 seconds from start
Band C will meet once every 80seconds or at times 80,.....from the start
So all three will meet once every 400 seconds , which is nothing but LCM ( 100,400,80) = 400
b) In an hour B and C will meet 3600/80 => 45 times
In an hour A and B meet 3600/100 => 36 times
So B and C meet 9 times more than A and B do.
