11. A man can walk uphill at the rate of $$2\frac{1}{2}$$ km/hr and downhill at the rate of $$3\frac{1}{4}$$ km/hr. If the total time required to walk a certain distance up the hill and return to the starting point was 4 hr 36 min, then what was the distance walked up the hill by the man ?
12. If a train runs at 40 kmph, it reaches its destination late by 11 minutes but if it runs at 50 kmph, it is late by 5 min only. The correct time for the train to complete its journey is :
13. A cyclist drove one kilometre, with the wind in his back, in 3 minutes and drove the same way back, against the wind, in 4 minutes. If we assume that the cyclist always puts constant force on the pedals, how much time would it take him to drive 1 km without wind ?
14. Two cyclists start from the same place in opposite directions. One goes towards north at 18 kmph and the other goes towards south at 20 kmph. What time will they take to be 47.5 km apart ?
15. A train approaches a tunnel AB. Inside the tunnel is a cat located at a point that is $$\frac{3}{8}$$ of the distance AB measured from the entrance A. When the train whistles, that cat runs. If the cat moves to the entrance A of the tunnel, the train catches the cat exactly at the entrance. If the cat moves to the exit B, the train catches the cat at exactly the exit. The ratio of the speed of the train to that of the cat is of the order :
16. With an uniform speed, a car covers a distance in 8 hours. had the speed been increased by 4 km/hr, the same distance could have been covered in 7 hr and 30 min. What is the distance covered ?
17. A star is 8.1 × 1013 km away from the earth. Suppose light travels at the speed of 3.0 × 105 km per second. How long will it take the light from the star to reach the earth ?
18. The speed of A and B are in the ratio 3 : 4. A takes 20 minutes more than B to reach a destination. In what time does A reach the destination ?
19. The average speed of a train in the onward journey is 25% more than that in the return journey. The train halts for one hour on reaching the destination. The total time taken for the complete to and fro journey is 17 hours, covering a distance of 800 km. The speed of the train in the onward journey is :
20. Ravi walks to and fro to a shopping mall. He spends 30 minutes shopping. If he walks at a speed of 10 km an hour, he returns home at 19.00 hours. If he walks at 15 km an hour, her returns home at 18.30 hours. How far must he walk in order to return home at 18.15 hours ?
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