**1.**Two friends A and B simultaneously start running around a circular track . They run in the same direction. A travels at 6 m/s and B runs at b m/s. If they cross each other at exactly two points on the circular track and b is a natural number less than 30, how many values can b take?

1. 3

2. 4

3. 7

4. 5

5. None of these

**2.**Three cars leave A for B in equal time intervals. They reach B simultaneously and then leave for Point C which is 240 km away from B. The first car arrives at C an hour after the second car. The third car, having reached C, immediately turns back and heads towards B. The first and the third car meet a point that is 80 km away from C. What is the difference between the speed of the first and the third car?

1. 60 kmph

2. 80 kmph

3. 20 kmph

4. 40 kmph

5. None of these

**3.**Three friends A, B and C decide to run around a circular track. They start at the same time and run in the same direction. A is the quickest and when A finishes a lap, it is seen that C is as much behind B as B is behind A. When A completes 3 laps, C is the exact same position on the circular track as B was when A finished 1 lap. Find the ratio of the speeds of A, B and C?

1. 5 : 4 : 2

2. 4 : 3 : 2

3. 5 : 4 : 3

4. 3 : 2 : 1

5. None of these

**4.**Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds. They meet at a point in between the two cities and then proceed to their respective destinations in 54 minutes and 24 minutes respectively. How long did B take to cover the entire journey between City Q and City P?

1. 60

2. 36

3. 24

4. 48

5. None of these

**5.**A swimming pool is of length 50 m. A and B enter a 300 m race starting simultaneously at one end of the pool at speeds of 3 m/s and 5 m/s. How many times will they meet while travelling in opposite directions before B completes the race?

1. Twice

2.Thrice

3. Once

4. 5 times

5. None of these

**6.**Car A trails car B by 50 meters. Car B travels at 45km/hr. Car C travels from the opposite direction at 54km/hr. Car C is at a distance of 220 meters from Car B. If car A decides to overtake Car B before cars B and C cross each other, what is the minimum speed at which car A must travel?

1. 36 km/hr

2. 45 km/hr

3. 67.5 km/hr

4. 18 km/hr

5. None of these

**7.**A and B stand at distinct points of a circular race track of length 120m. They run at speeds of a m/s and b m/s respectively. They meet for the first time 16 seconds after they start the race and for the second time 40 seconds from the time they start the race. Now, if B had started in the opposite direction to the one he had originally started, they would have meet for the first time after 40 seconds. If B is quicker than A, find B’s speed.

1. 3 m/s

2. 4 m/s

3. 5 m/s

4. 8 m/s

5. None of these

**8.**City A to City B is a downstream journey on a stream which flows at a speed of 5km/hr. Boats P and Q run a shuttle service between the two cities that are 300 kms apart. Boat P, which starts from City A has a still-water speed of 25km/hr, while boat Q, which starts from city B at the same time has a still-water speed of 15km/hr. When will the two boats meet for the first time? (this part is easy) When and where will they meet for the second time?

1. 7.5 hours and 15 hours

2. 7.5 hours and 18 hours

3. 8 hours and 18 hours

4. 7.5 hours and 20 hours

5. None of these

**9.**Cities M and N are 600km apart. Bus A starts from city M towards N at 9AM and bus B starts from city N towards M at the same time. Bus A travels the first one-third of the distance at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmpr. Bus B travels the first one-third of the total time taken at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmph. When and where will the two buses cross each other?

1. 300 kms from A

2. 280 kms from A

3. 305 kms from A

4. 295 kms from A

5. None of these

**10.**A car of length 4m wants to overtake a trailer truck of length 20m travelling at 36km/hr within 10 seconds. At what speed should the car travel?

1. 12 m/s

2. 14.8 m/s

3. 12.4 m/s

4. 7.6 m/s