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Assume the perimeter of the track=x

Speed of first person= \(\frac{2*x}{1}\)=2x
Speed of second person= \(\frac{3*x}{1}\)=3x

Time taken by them to meet first time=\(\frac{x}{(2x+3x)}\)=\(\frac{1}{5}\) hrs= 12 minutes

Number of times they cross each other before 9:30AM= [\(\frac{1.5*60}{12}\)]=[7.5]=7


Hovkial
Two people are walking around a circular track. They start at 8 A.M. from the same point but travel in opposite directions. The first person walks at a speed of two rounds per hour and the second person walks at a speed of three rounds per hour. How many times will they cross each other before the clock shows 9:30 A.M.?

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9
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Consider the track is 1 km.
person 1 speed 2km/hr
person 2 speed 3km/hr

Relative speed ( Opposite direction : Add the speeds )

(2 + 3) km/hr = 1 km /Time ( hr )
Time = 1/5 hr = 12 mins ( They meet at every 12 mins )

Hence 8 to 9:30 : 90 mins : hence 7 times
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