51. An individual is cycling at a speed of 25 km per hour. He catches his predecessor who had started earlier in two hours. What is the speed of his predecessor who had started 3 hours earlier ?
52. A 6 cm long cigarette burns up in 15 minutes if no puff is taken.For every puff, it burns three times as fast during the duration of the puff.If the cigarette burns itself in 13 minutes, then how many puffs has the smoker taken if the average puff lasted 3 seconds?
53. An old man driving bike at 80 km per hour. However being sugar patient, old man could not travel continuously. He takes small breaks each of 2 minutes for every 15 minute of his drive. How much distance the old man will cover in 90 minutes?
54. Two trains start simultaneously from two stations Howrah and Delhi, respectively towards each other on the same track. The distance between the two stations is 560 km and the speeds of trains are 30 kmph and 40 kmph.
Simultaneously with the trains, a sparrow sitting on the top of one of the train starts towards the other and reverses its direction on reaching the other train and so on. If the speed of sparrow is 80 kmph then the distance that the sparrow lies before being crushed between the train is :
55. Due to the technical snag in the signal system two trains start approaching each other on the same track from two different stations, 240 km away each other. When the train starts a bird also starts moving to and fro between the two trains at 60 kmph touching each train each time. The bird initially sitting on the top of the engine of one of the trains and it moves so till these trains collide. If these trains collide one and half hour after start, then how many kilometers bird travels till the time of collision of trains?
56. A man goes to the fair with his son and dog. Unfortunately man misses his son which he realizes 20 minutes later. The son comes back towards his home at the speed of 20 m/min and man follows him at 40 m/min. The dog runs to son and comes back to the man to show him the direction of his son. He keeps moving to and fro at 60 m/min between son and father, till the man meets the son. What is the distance traveled by the dog in the direction of the son?
57. A tiger is 50 of its own leaps behinds a deer. The tiger takes 5 leaps and per minutes to the deer's 4. If the tiger and the deer cover 8 m and 5 m per leap respectively, what distance will the tiger have to run before it caches the deer?
58. A candle of 6 cm long burns at the rate of 5 cm in 5 hour and an another candle 8 cm long burns at the rate of 6 cm in 4h. What is the time required to each candle to remain of equal lengths after burning for some hours, when they starts to burn simultaneously with uniform rate of burning?
59. A man walking at the speed of 4 km/hr,cross a square field diagonally in 3 minutes.The area of the field is?
60. A train approaches a tunnel AB. Inside the tunnel a cat located at a point i.e. $$\frac{5}{{12}}$$ of the distance AB measured from the entrance A. When the train whistles the Cat runs. If the cat moves to the exit B, the train catches the cat exactly the exit. The speed of the train is greater than the speed of the cat by what order ?
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