Time & Distance Test 3

1. P and Q start running a race on the given track as shown in figure: Where AC and BC are mutually perpendicular and CD is the median of triangular paths ABC. BC is 100 km longer than that of AC, and CD is 250 km. The speeds of P and Q are 30 km/h and 40km/h, respectively and their respective paths of running are CADC and CBDC. After how much time they reverse their speeds so that they return C at the same time?

2. A candle of 6 cm long burns at the rate of 5 cm in 5 h and another candle of 8 cm long burns at the rate of 6 cm in 4 h. What is the time required by each candle to remain of equal lengths after burning for some hours, when they start to burn simultaneously with uniform rate of burning?

3. Resting 9 hrs. a day Rajesh kuma travels a certain distance in 40 days. Resting double the time how many days will he take to travel double the distance at double the speed ?

4. Resting 4 hrs a day Rajesh kuma travels a certain distance in 60 days. Resting thrice the time how many days will he take to travel thrice the distance at thrice the speed?

5. A officer goes to office from his home, which is 8 km apart. His speed is 4 km/h. After 5 min the feels that he left some important documents at home. He returns to home and now he travels with fast speed towards the office, and reaches office on time. Find his increase speed?

6. Rajesh kumar can see apprx. d km far from the h metre above high level in sea water. And the relation between d and h is 2d2 = 25 h. Then find from how much high level Rajesh kumar can see 10 km?

7. Two men are standing on opposite ends of a bridge of 1200 metres long. If they walk towards each other at the rate of 5m/minute and 10m/minute respectively, in how much time will they meet each other?

8. A constable is 114 metres behind a thief. The constable runs 21minute in a metres and the thief 15 metres in a minute, In what time will the constable catch the thief ?

9. A walks at a uniform rate of 4 km an hour; and 4 hours after his start, B bicycles after him at the uniform rate of 10 km an hour. How far from the starting point will B catch A ?

10. A train starts from A at 7 a.m. towards B with speed 50 km/h. Another train from B starts at 8 a.m. with speed 60 km/h towards A. Both of them meet at 10 a.m. at C. The ratio of the distance AC to BC is :

11. A thief, who was chased by a policeman was 100 metres ahead of the policeman initially. If the ratio between speeds of the policeman and the thief is 5 : 4, then how long thief would have covered before he was caught by the policeman?

12. A jeep is chasing a car which is 5 km ahead. Their respective speeds are 90 km/ hr and 75 km/hr. After how many minutes will the jeep catch the car?

13. P and Q are 27 km away. Two trains with speeds of 24 km/ hr and 18 km/hr respectively start simultaneously from P and Q and travel in the same direction. They meet at a point R beyond Q. Distance QR is:

14. A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km per hour and 11 k.m. per hour respectively. What is the distance between them after 6 minutes?

15. A tiger is 50 of its own leaps behind a deer. The tiger takes 5 leaps per minute to the deer’s 4. If the tiger and the deer cover 8m and 5m per leap respectively, what distance will the tiger have to run before it catches the deer ?

16. Two men start walking from A and B, 72 km distance toward each other at same time. The speed of first person is 4 km/ h. While the other one starts at 2 km/h and increases his speed every hour by 1/2 km/h when will they meet ?

17. Two car start from same place at same time. Speed of first car is 10 km/h and the speed of IInd car is 8 km/h and it increase its speed 1/2 km/h after each hour. After how much distance the second overtake the first :

18. A hound is chasing a rabbit, intially the rabbit was 125 his own leaps ahead the Hound. A hound takes 3 leaps for every 4 leaps of a rabbit. A rabbit and a hound covers 1.75 m and 2.75 m distance in a leap respectively. Then in how many leaps the hound will catch the rabbit?

19. A man can see 400 m in a fog. When he was travelling at a speed of 4 km/hr, he saw a train was coming behind him which was passing by the side of man and disappeared after 3 minutes. If the length of train is 200 m then find the speed of the train?

20. A hare was 180 m ahead from a hound after seeing the hound, hare started running at 9 km/h. After 1 min the hound started chasing the hare at a speed of 12 km/h. Find the distance travelled by the hound if the hound will catch the hare from the place where the hound standing?