Q.1 Vinay and Vamsi start running at the same time around a circular track with their speeds in the ratio of 5 : 3. If the distance covered in one round is 1½ km., what is the distance covered by Vinay when he passes Vamsi for the seventh time?

Q.2 The local shuttle service trains which travel at a uniform speed run at regular intervals. Brinda, walking down along the railway track at uniform speed found that every 6 min there is a local train coming in the opposite direction and every 12 min there is a local train overtaking her from behind. What is the time gap between one local train passing a stationary point on the railway route and the immediately next local train in the same direction passing the same point?

Q.3 A and B start from two points P and Q respectively with uniform velocities. A is headed towards Q and B towards P. P and Q are separated by a distance of 2000 km. A rests whenever B is on the move and B rests whenever A is on the move. A’s speed is 40 km/hr. If A starts first and reaches the destination in 60 hrs, then find the least time that B would take to reach his destination after A makes a start, given that B’s speed is 50 kmph.

Q.4 A bird starts flying from a place O towards B via A. There is no wind resistance from O to A. But there is wind resistance (in the form of uniform wind velocity) between A and B. To travel from O to B the bird takes 12 minutes, whereas to travel from B to O (via A) the bird takes 14 minutes. Had there been wind resistance between O and A also (which equals, that between A and B), the bird would have taken only 11 minutes to travel from O to B. O, A and B are in a straight line. If there was the same wind resistance between O and A as between A and B, what would be the time taken by the bird to travel from B to O?

Q.5 A bird starts flying from a place O towards B via A. There is no wind resistance from O to A. But there is wind resistance (in the form of uniform wind velocity) between A and B. To travel from O to B the bird takes 12 minutes, whereas to travel from B to O (via A) the bird takes 14 minutes. Had there been wind resistance between O and A also (which equals, that between A and B), the bird would have taken only 11 minutes to travel from O to B. O, A and B are in a straight line. What is the ratio of the distance OA to the distance AB?

Q.6 Abhay, Ajay and Vijay wish to travel from town A to town B. They have one motorcycle which can be driven by any of them but can carry only two persons at a time. The distance between the two towns is 105 km and the speed at which they can walk is 5 kmph. If the speed of the motorcycle is 35 kmph then what is the total distance that the bike travels if they travel such that all three of them reach town B simultaneously?

Q.7 A man set out at noon to walk from Khalagpur to Danapur, and a friend of his started at 2 pm on the same day to walk from Danapur to Khalagpur. They met on the road at five minutes past four o’clock, and each man reached his destination at exactly the same time. Can you say at what time they both reached their respective destinations?

Q.8 A clock is observed. The hour hand is exactly at the minute mark, and the minute hand is six minutes ahead of it. Later, the clock is observed again. This time the hour hand is exactly on a different minute mark, and the minute hand is seven minutes ahead of it. How much time has elapsed between the first and the second observation?

Q.9 You begin your vacation at Village A and travel to Village B. From Village B you move on to Village C and then to Village D. You leave Village D and return back to Village A. Your round trip was 54 km and the distance between each village is a whole number. The distance between Village A and Village B is greater than between Village B and Village C Also, if you went directly from Village B to Village D, it would be a distance of 12 km. What is the distance from Village C to Village D?

Q.10 There are two concentric circular tracks of lengths 200 km. and 300 km. A car moves on the outer track at the speed of 50 kmph in the clock wise dirdction. A scooter moves on the inside track in the anti-clockwise direction at a speed of 60 kmph. If both start from the north most point of the track at the same time and the first person to travel 1200 km does so and stops, then how many times has he crossed the other person in the time in which he was moving?