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### Mathematical Skills | Time, Speed and Distance

 Q. No. 1: From a point P, on the surface of radius 3cm, two cockroaches A and B started moving along two different circular paths, each having the maximum possible radius, on the surface of the sphere, that lie in the two different planes which are inclined at an angle of 45 degree to each other. If A and B takes 18 sec and 6 sec respectively, to complete one revolution along their respective circular paths, then after how much time will they meet again, after they start from P? A : 27 sec B : 18 sec C : 9 sec D : 24 sec Solution
 Q. No. 2: P and Q travels from D to A and break journey at M in between. Somewhere between D and M, P asks "how far have we travelled?" Q replies,"Half as far as the distance from here to M".Somewhere between M and A, exactly 300km from the point where P asks the first question, "How far have we to go?" Q replies, "Half as far as the distance from M to here". The distance between D and A is A : 250 km B : 450 km C : 350 km D : 500 km Solution
 Q. No. 3: Two motorist A and S are practicing with tow different speed cars: Ferrari and Maclarun, on the circular racing track, for the car racing tournament to be held next month. Both A and S start from the same point on the circular track. A completes one round of the track in 1 min and S takes 2 min to complete a round. While A maintains same speed for all the rounds, S halves his speed after the completion of each round. How many times A and S will meet between the 6th round and the 9th round of S (6th and the 9th round is excluded)? Assume that the speed of S remains steady throughout each round and changes only after the completion of that round. A : 260 B : 347 C : 375 D : 382 Solution
 Q. No. 4: Laila drives to the station each day to pick up her husband Manju, who usually arrives on a train at 6o’clock. Last Monday, Manju finished work earlier, caught an earlier train and arrived at the station at 5 ‘o clock. He started to walk home and eventually met Laila who drove him the rest of the way, getting home 20 minutes earlier than usual. On Tuesday, he again finished early and found himself at the station at 5 : 30. Again he began to walk home, again he met Laila on the way, and she drove him home the rest of the way, Assume constant speed throughout with no wasted time for waiting, backing of the car etc. How earlier than the usual time were theory home on Tuesday? A : 6 minutes B : 8 minutes C : 10 minutes D : 12 minutes Solution
 Q. No. 5: In a 3600 m race around a circular track of length 400m, the faster runner and the slowest runner meet at the end of the fourth minute, for the first time after the start of the race. All the runner maintains a uniform speed throughout the race. If the faster runner runs at thrice the speed of the slowest runner. Find the time taken by the faster runner to finish the race. A : 36 min B : 24 min C : 16 min D : 12 min Solution
 Q. No. 6: Three athletes A,B and C run a race, B finished 24 meters ahead of C and 36 m ahead of A, while C finished 16 m ahead of A. If each athlete runs the entire distance at their respective constant speeds, what is the length of the race? A : 108 m B : 90 m C : 80 m D : 96 m Solution
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