Q1. A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 264 metres long in 20 seconds. The length of the train (in metres) is:
Sol. Let the length of train = L meter
And speed of train = S m/s
L = S × 8
S = L/8 m/s
S = (L + 264)/20
L = 264 ×2/3
L = 176 meter
Q2. A 150 metre long train crosses a 500 metre long bridge in 30 seconds. What time will it take to cross a platform 370 metre long?
(a) 36 seconds
(b) 30 seconds
(c) 24 seconds
(d) 18 seconds
Sol. Train travels 150 + 500 meter in 30 second
Speed of train = 650/30
= 65/3 m/s
Now, time take to cross a platform 370 metre long
= 24 sec.
Q3. A passenger standing on a railway platform observes that a train going in one direction takes 4 seconds to pass him. Another train of same length going in opposite direction takes 5 seconds to pass him. The time taken (in seconds) by the two train to cross each other will be:
(d) None of these
Sol. Let the length of each train be x metre and the speeds of the trains are S1 and S2 respectively.
Now, Required time = 2x/(x/4 + x/5)
[∴ Trains are moving opposite] = 40/9 seconds
Q4. A passenger sitting in a train of length l m, which is running with speed of 60 km/h passing through tow bridges, notices that he crosses the first bridge and the second bridge in time intervals which are in the ratio of 7 : 4 respectively. If the length of first bridge is 280 m, then the length of second bridge is:
(a) 490 m
(b) 220 m
(c) 160 m
(d) Can’t be determined
Sol. Passenger sitting in a train pass through two bridges then the train will travel the only length of the bridge.
So, ratio of length of bridge = ratio of time to pass the bridge. (Distance α time)
= 7: 4
So, length of second train = (280 × 4)/7
= 160 metre.
Q5. Two guns are fired from the same place at an interval of 6 minutes. A person approaching the place observes that 5 minutes 52 seconds have elapsed between the hearing of the sound of the two guns. If the velocity of the sound is 330 m/sec, the man was approaching that place at what speed (in km/hr)?
Sol. Difference of time = 8 second
So, distance covered by 352 s (5 × 60 + 52) second by man
= distance covered by sound in 8 second
S × 352 = 330 × 8
Here S is the speed of man in m/s
S = 15/2 m/s
So, speed in km/hr
S = 15/2×18/5=27 km/hr
Q6. The distance between Delhi and Patna is 1000 km. A train P leaves Delhi for Patna at 5 pm at 150 km/hr. Another train Q leaves Patna for Delhi at 6.30 pm at 100 km/hr. How far from Delhi will the two trains meet?
(a) 690 km
(b) 310 km
(c) 590 km
(d) 465 km
Q7. Two cyclists start simultaneously towards each other from A and B which are 28 km apart. An hour later they meet and keep pedaling with the same speed without stopping. The second cyclist arrives at B, 35 minutes later than the first arrives at A. Find the speed of the cyclist who started from B.
(a) 12 km/h
(b) 16 km/h
(c) 15 km/h
(d) 10 km/h
Q8. A and B are two friends. A lives at a place P and B lives at another place Q. Everyday A goes to Q to meet B at 120 km/h. Thus, he takes 3 hours. On a particular day B started to meet A so he moved towards P. On that day A took only 2 hours to meet B on the way instead at Q. What is the ratio of the speeds of A is B?
(d) None of these
Q9. Two friends started walking simultaneously from points A and B towards each other. 144 minutes later the distance between them was 20% of the original distance.after how many time they meet each other
Q10. The speed of a car during the second hour of its journey is thrice that in the first hour. Also its third hours speed is the average speed of the first two hours. Had the car travelled at the second hours speed during all the first three hours, then it would have travelled 150 km more. Find the percentage reduction in time in the second case for the first three hours:
Q11. In a stream, B lies in between A and C such that it is equidistant from both A and C. A boat can go from A to B and back in 6 h 30 minutes while it goes from A to C in 9 h. How long would it take to go from C to A?
(a) 3.75 h
(b) 4 h
(c) 4.25 h
(d) 4.5 h
Q12. A boat can row 66 km downstream and 56 upstream in 7 hours. And it can row 88 km downstream and 28 km upstream in 6 hours. Then find the time taken by boat to row 72 km in still water, and also find if a paper boat puts in the stream, then how much far away it will be after 1 hour 30 minutes?
(a) 4 hrs, 6 km
(b) 12 hrs, 4 km
(c) 16 hrs, 25 km
(d) None of these
Q13. In the river of Yamuna the distance between two points is 80 km. A boat which rows 13 km/h in still water goes from the first point to the second and returns to starting point in 13 hours. Then what is the speed of current?
(a) 5 km/hr
(b) 2 km/hr
(c) 3 km/hr
(d) None of these
Q14. A can give 40 metres start to B and 70 metres to C in a race of one kilometer. How many metres start can B give to C in a race of one kilometer?
Q15. A man travels 40 km by train at 20 km/hr, 60 km by car at 10 km/h, 30 km by bus at 15 km/h, 80 km by airplane at 25 km/h and 120 km by ship at 30 km/hr. Then find out the average speed of man during the entire journey, and also find out in how many hours he can travel 825 km distance by the same average speed?
Sol. Average speed = (Total distance)/(Total time)
Time taken by train = 40/20 = 2 hours
Time taken by Car = 60/10 = 6 hours
Time taken by bus = 30/15 = 2 hours
Time taken by Airplane = 80/25 = 3.2 hours
Time taken by Ship = 120/30 = 4 hours
Average speed = (40 + 60 + 30 + 80 + 120)/(2 + 6 + 2 + 3.2 + 4)
=330/17.2=825/43=19 8/43 km/hr
Average speed = 198/43 km/hr
(ii) Time taken to travel 825 km
=825/825×43 = 43 hours