A car travels first half distance between two places with a speed of 40km/hr and rest of the half distance with a speed of 60km/hr. The average speed of the car is
Answer: A Let the total distance covered be S km. Total time taken = S/(2*40) + S/(2*60) = 5S/240 hr Average speed = S* 240/5S = 48 km/hr
Q. No. 14:
A jet plane is rising vertically with a velocity of 10m/s. It has reached a certain height when the pilot drops a coin, which takes 4sec to hit the ground. Assuming that there is no resistance to the motion of the coin, the height of the place and the velocity of the coin on impact with the ground are
Answer: B The coin will move up with the initial velocity of 10m/s till it comes to rest. Time taken is given by 0 = 10- 9.8 t => t= 10/9.8 s Time taken to reach the ground from the highest point => 4 - 10/9.8 = 29.2/9.8 sec Velocity of coin on impact = 0 + 29.2/9.8 * 9.8 = 29.2 m/s If 'h' is the height from which the coin dropped. Then, 29.22 - 102 = 2*9.8*h => h = 38.4 m
Q. No. 15:
A train starts from Delhi at 6:00 am and reaches Ambala cantt. at 10am. The other train starts from Ambala cantt. at 8am and reached Delhi at 11:30 am, If the distance between Delhi and Ambala cantt is 200 km, then at what time did the two trains meet each other?
Answer: C Average speed of train leaving Delhi = 200/4 = 50km/hr Average speed of train leaving Ambala cantt. = 200*2/7 = 400/7 km/hr By the time the other train starts from Ambala cantt, the first train had travelled 100km Therefore, the trains meet after 200/ (50 + (400/7)) = 14/15 hr = 14/15 * 60 = 56 minutes Hence they meet at 8:56am
Q. No. 16:
A ship, 40km from the shore, springs a leak which admits 15/4 tonnes of water in 12 min. 60 tonnes would suffice to sink her, but the ship's pumps can throw out 12 tonnes of water in one hour. Find the average rate of sailing, so that she may reach the shore just as she begins to sink.
Answer: D Amount of water admitted by the leak in one hour = 15/4 * 60/12 = 75/4 tonnes. Net water in the ship in one hour = 75/4 -12 = 27/4 L Number of hours in which the danger level of 60 tonnes of water is in the ship => 60*4/27 = 80/9 hr Required average speed of the ship to reach the shores safely => 40/80 * 9 = 9/2 km/hr
Q. No. 17:
A boatman rows to a place 45 km distant and back in 20 hour. He finds that he can row 12 km with the stream in the same time as 4km against the stream. Find the speed of the stream.
Answer: A Ratio of time taken for up and down = 3:1. Out of 20 hr he took 15 hr for up and 5 for down.Speed up = 45/15 =3 and down =45/5 =9. Hence speed of stream = (9-3)* 1/2 = 3 km/hr
Q. No. 18:
A man can row 4.5 km/hr in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of the stream.
Answer: C Let the speed o the current be xkm/hr Thus upward speed = (4.5 -x) km/hr and downward speed = (4.5 -x) km/hr Let distance travelled be y, then y/(4.5-x) = 2y/(4.5+x) => x= 1.5 km/hr