Rahul can row a certain distance downstream in 6 hour and return the same distance in 9 hour. If the speed of Rahul in still water is 12 km/hr, Find the speed of the stream.
Answer: B Let the speed of the stream be x km/hr Thus, downward stream = (12 + x) and upward stream = (12 -x) suppose the distance travelled be y Given, y/(12+x) =6 and y/(12-x) =9 On solving these two equations we get x= 2.4 km/hr
Q. No. 20:
A man sitting in train travelling at the rate of 50 km/hr observes that it takes 9 sec for a goods train travelling in the opposite direction to pass him. If the goods train is 187.5m long. Find its speed
Answer: D Let the speed of goods train be x km/hr. Then, (50 + x)* 5/18 = 187.5/9 => x= 25 km/hr
Q. No. 21:
A train 120m in length passes a pole in 12sec and another train of length 100m travelling in opposite direction in 10sec. Find the speed of the second train in km per hour.
Answer: A Let the speed of the train be x km/hr Then, 120 = x * 5/18 * 12 => x= 36 km/hr Let speed of the other train be y km/hr Then, relative speed in opposite direction = (y+36) * 5/18 (120+100) = (y+36) * 5/18 * 10 y = 43.2 km/hr
Q. No. 22:
A good train and a passenger train are running on parallel tracks in the same direction. The driver of the goods train observes that the passenger train coming from behind overtakes and crosses his train completely in 60 sec. Where as a passenger on the passenger train marks that he crosses the goods train in 40 sec. If the speeds of the trains be in the ratio 1:2. Find the ratio of their lengths.
Answer: B Let the speeds of the two trains be s and 2s m/s respectively. Also, suppose that the lengths of the two trains are P and Q metres respectively. Then, (P+Q)/(2s-s) =60 .......(i) and P/(2s-s) = 40................(ii) On dividing these two equation we get (P+Q)/P = 60/40 P:Q = 2:1
Q. No. 23:
In a race, the speeds of A and B are in the ratio 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is
Answer: C Ratio of speeds = 3:4 Distance remaining constant, the ratio of time taken = 4:3 A takes 0.5 hours more than B Hence time taken by A = 4* 0.5 = 2 hour.
Q. No. 24:
Two places A and B are separated by a distance of 200 m. Ajay and Jay have to start simultaneously from A, go to B and return to A. In 10 s they meet at a place 10m from B. If Ajay is faster than Jay, in how much time, after they start, will Ajay return to A?
Answer: C Since Ajay is faster than Jay and they start together, to meet at 10m from B, Ajay would have covered a distance from A to B and would meet Jay on his way back to A. Jay would be on his way from A to B. So, Ajay covers 200+10 = 210 m in 10 sec Hence, Ajay's speed = 21 m/sec So he will take 190/21 sec to cover the remaining 190 m. The time required for Ajay to reach A will be => 10 + 190/21 = 400/21 sec.