A boat covers a distance of 30km downstream in 2 hour while it takes 6 hour to cover the same distance upstream. What is the speed of the boat in km/hr.
Answer: C Let b and s be the speed of boat and stream respectively. As per the given conditions, 30/(b+s) = 2............(i) And, 30/(b-s) = 6............(ii) From eq (i) and (ii), s = 5 and b = 10 km/hr.
Q. No. 32:
A cyclist drove one kilometre, with the wind in his back, in three minutes and drove the same way back, against the wind in four minutes. If we assume that the cyclist always puts constant force on the pedals, how much time would it take him to drive one kilometer without wind ?
Answer: B Let the speed of the cyclist be xkm/h and wind be ykm/h. 1/(x+y) = 3/60 => x+y = 20..........(i) And, 1/(x-y) = 4/60 => x-y = 15..........(ii) On solving both the equations we get, x= 35/2, y=5/2 Now, time taken by cyclist without wind = 2/35 * 60 = 24/7 min.
Q. No. 33:
Two identical trains A and B running in opposite direction at same speed tale 2 min to cross each other completely. The number of bogies of A are increased from 12 to 16. How much more time would they now require to cross each other ?
Answer: D Total initial bogies is 12+12 = 24 Additional bogies = 16-12 =4 24 bogies take 2 minutes. 4 bogies will take (2*60)/(24) * 4 = 20 sec.
Q. No. 34:
P and Q start running in opposite directions (towards each other) on a circular track starting at diametrically opposite points. They first meet after P has run for 75m and then they next meet after Q has run 100 m after their first meeting. Assume that both of them are running a constant speed. The length of the track (in metre) is :
Answer: D Both P and Q comes equal distance as both have equal constant speed. Total distance covered by Q = 75+100 = 175 m Hence, total tracks length = 175*2 = 350 m.
Q. No. 35:
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 am and travel towards B at 20 km/hr speed. Another train starts from B at 8 am and travel towards A at 25 km/hr speed. At what time will they meet ?
Answer: B A................C..........................B 7am.....................................8am AC = 20 km, CB =90 km Distance traveled in 1 hour = 20 km Remaining distance = 110-20 = 90 km Time taken = Distance/Relative speed = 90/(20+25) = 2 hours. So, time = 8 am + 2 = 10 am.
Q. No. 36:
A train running at the speed of 20m/s crosses a pole in 24 sec less than the time it requires to cross a platform thrice its length at the same speed. What is the length of the train?
Answer: D Let the length of the train be x m. So, the length of the platform = 3x m. Time taken in crossing the platform = 4x/20 sec. Time taken in crossing the pole = x/20 sec. => x/20 + 24 = 4x/20 => x = 160 m.