A bike departs from point X at 9:00 AM toward point Y, traveling at a speed of 45 km/h. Two hours later, a car starts from point X toward point Y at a speed of 60 km/h. The car overtakes the bike at point Z, located between X and Y. After overtaking the bike, the car reaches point Y in 15 hours and immediately begins its return journey. The car and the bike meet again at point W. Determine the distance between points W and Z.

According to the question, Time taken by car to overtake bike = 2 x 45 / (60 – 45) = 6 hours After 6 hours from start, both are at point Z. Distance between point Z and point Y = 60 x 15 = 900 km In 15, hours distance travelled by bike = 15 x 45 = 675 km Now at this point, the bike is running towards point Y and the car is towards X. Now, time is taken by car to reach at point W after reaching point Y = (900 – 675)/ (60 + 45) = 15/7 hours Distance between point W and Z = 900 – 15/7 x 60 = 771.42 km Hence answer is option A