INFANT JESUS GROUP OF ENGINEERING COLLEGES PLACEMENT TRAINING – QUANTITATIVE APTITUDE TIME AND DISTANCE Results ;
1.General 1) Speed = distance / time 2) Speed and distance are directly proportional .if the speed is doubled in the same time distance travelled will also be doubled 3) Distance and time are directly proportional . if the distance is doubled at the same speed , time taken will also be doubled do ubled 4) Time and speed are inversely proportional. If the speed is doubled time taken to travel the same distance will be half the original o riginal time 5) Speed = 1 m/s = 18/5 km/r 6) Speed = 1 km/hr = 5/18 m/s
1) 2) 3) 4) 5)
6)
2 .Train problem Time taken by a train Of length l meter to pass a stationary object of length b meter is the time taken to cover (l+b) meters Time taken by a train Of length length l meter to pass a pole or standing man or post is the time taken to cover l meters If two trains are moving in the same direction at speds u m/s m/s and v m/s where u> v then their relative speed is ( u – v ) m/s If two trains are moving moving in the opposite direction at speds u m/s and v m/s m/s then their relative speed is ( u +v ) m/s If two trains of length a meter and b meter are moving in the same direction at speeds u m/s and v m/s where u> v then the time taken by the faster train to cross the slower train is a+ b / u-v s If two trains of length a meter and b meter are moving in the opposite direction at speeds u m/s and v m/s then the time taken by the trains to cross each other is a+ b / u+v s
3. BOAT PROBLEMS 1) If b is the speed of the boat and s km/hr is the speed of the stream then the speed along the stream (downstream) is b+s km/hr and the speed against the stream (upstream) is b-s km/hr 2) If speed downstream is a km/hr and speed upstream is b km/hr then Speed in still water = a+b /2 km/hr Speed of stream = a-b /2 km/hr
4. RACES 1) Start : if before the the start of the race A is at the starting point and B is ahead of A by 10 meters, then we say that A gives g ives B a start of 10 meters 2) in a 100m race A can give B a start of 10m means means that when A runs 100m , B runs 90m 5. CIRCULAR TRACKS 1) FIRST MEETING AT STARING POINT : when 2 or more ladies start moving simultaneously from the same point on a circle in the same direction around the t he circle they all will meet again at the starting po int after time T where Tis the lcm of the times taken by each body to take one complete round 2) FIRST MEETING : when 2 ladies start moving simultaneously from the same point on a circle in the same direction / opposite direction around the circle they meet meet for the first time after after time T where t= circumference of the circle / relative re lative speed when 3 or more ladies start moving simultaneously from the same point on a circle in the same direction around the circle , they they all meet for the first time after time T where Tis the lcm of the times taken by the faster to meet each of the slower runners . 1. A 150 metres long train crosses another train traveling in the opposite direction in 10 seconds. If the length of the second train is 200 metres. What are the speeds of the trains if both the trains have equal speed (in Km/h)? a) 60 b) 63 c) 35 d) 70 Answer : b) 63 Solution : Distance travelled in 10 secs = 150 +200 m Distance travelled travelled in 1 hr =350 x 60 x60 /10 m = 350 x 60 x60 / ( 10 x 1000) km = 126 km When the trains trains travelled in opposite direction direction relative velocity velocity = v1 + v2 v1 = v2 = v 2v = 126 km
V = 63km/hr 2. A 125 metres long train overtakes another 100 metres long train in 15 seconds. If the speed of the slower train is 18 Km/h. Find the speed of the faster train. a) 72 Km/h b) 70 Km/h c) 20 Km/h d) 22 Km/h. Answer : a) 72 Km/h
Solution : v1 - v2 = (125 + 100/ 15)( 60 x60 / 1000 ) =
v1 – 18 = 15 x 6 x 6 / 10 = 54 v1= 54 + 18 = 72 since the trains travel in the same direction relative velocity = v1 - v2 3. Without any stoppages, a train travels at an average speed of 75Km/h and with stoppages, it covers the same distance at an average speed of 60 Km/h. How many minutes per hour does the train stop? a) 10 minutes b) 15 minutes c) 12 minutes d) 18 minutes Answer : c) 12 minutes Solution : time taken to travel 75km = 1 hr = 60m Time taken to travel 60km = 60 x 60 / 75 = 48m The train stops 60 -48 = 12m /hr
4. Speed of a boat in still water is 10 Km/h. The boat travels downstream through 24 Km in 2 hours. In what time will it cover the same distance upstream? a) 3 hrs b) 5 hrs c) 6 hrs d) 7 hrs Answer : a) 3 hrs Solution : Speed of boat b = 10km/hr Speed of boat upstream = b – s
Speed of boat upstream = b – s The boat travels downstream through 24km is 2 hr B+s = 12 km/hr S= 2 km/hr S = 8km/hr Time taken to travel 24km upstream = 24/8 = 3hr 5. The speed of the current is 2 Km/hr. A boat travels 8 Km upstream and returns to starting point in 3 hrs. What is the speed of the boat in still water? a) 3 Km/h b) 5 Km/h c) 6 Km/h d) 7 Km/h. Answer : c) 6 Km/h Solution : s = 2km/hr Speed of boat upstream = b – s Speed of boat downstream = b + s 8/ b-s + 8 / b+s = 3 Try with answer is b=6
6. In what time would a train of 80 metres long, traveling at the speed of 40 Km/h cross a platform 100 metres long? a) 18 sec b) 16.2 sec c) 9 sec d) 7.2 sec Answer : b) 16.2 sec Solution : distance travelled = 80m + 100m = 180m Speed = 40 km/hr = 40 x 50 /3 m/min Time taken = 180 x 3 x 60 / 40 x 50 secs = 81/5 = 16.2 sec
7. Due to a technical snag, a train travels at three-fourth of its usual speed. How much longer will it take to cover the distance that it normally covers in one hour? a) 15 minutes b) 30 minutes c) 45 minutes d) 20 minutes Answer : d) 20 minutes Solution : let the usual speed be s, usual time t Speed = ¾ s Time = 4/3 t Time = 4/3 hr = 1hr 20 min
8. Ashok traveled 1200 Km by air, which accounts for two-fifth of his total journey. Further, one third of the journey was by car and the rest of it was by train. What is the distance traveled by Ashok by train? a) 480 Km b) 1800 Km c) 1600 Km d) 800 Km Answer : d) 800 Km Solution : 2/5 D =1200 D= 3000KM Distance travelled by train = [1 – (2/5 +1/3 ) ] D [1 – (11/15)] D 4 x 3000 / 15 = 800km 9. A cyclist travels two third of the total distane of his journey at the speed of 20 Km/h. while the rest of it at the speed of 10 Km/h. What is the overall speed of the entire journey? a) 12.5 Km/h b) 16 Km/h c) 17.5 Km/h d) 15 Km/h. Answer : d) 15 Km/h. Solution : D be the distance travelled Time taken to cover 2/3 D at a speed of 20 km/hr = 2/3 D /20 Time taken to cover 1/3 D at 10km/hr = 1/3D / 10 Speed = distance / time taken = D /( 2/3 D/20
+ 1/3 D/10 )
30 / 2 = 15 KM/HR
10. A streamer going downstream takes four hours to cover the distance that it covers in 5 hours while going upstream. If the speed of the stream is 2 Km/h What is the speed of the streamer in still water? a) 15 Km/h b) 18 Km/h c) 9 Km/h d) 12 Km/h. Answer : b) 18 Km/h Solution : LET X be the distance covered X = ( b -2 ) 5 X= (b+2) 4 (b-2)5 = ( b+2) 4 b = 8 +10 = 18 11. The distance between two station A and B is 220 Km. A train leaves station A towards B at the speed of 80 Km/h. Half an hour later another train leaves B towards A at the speed of 100 Km/h. At what distance from A will the two trains meet? a) 120 Km b) 130 Km c) 140 Km d) 160 Km Answer : a) 120 Km Solution : relative velocity = 180 km Time taken = 1 hr Distance from A = 120km 12. A person rows one kilometer down in the stream in 10 minutes and returns in 30 minutes. What is the velocity of the current? a) 3 Km/h b) 6 Km/h c) 2 Km/h d) 4 Km/h. Answer : c) 2 Km/h Solution : b+s= 1/10 km/ min = 6 km /hr b-s = 1/30 km/min = 2 km/hr s= 6-2 / 2 = 2km/hr
13. A train passes over a 1000 metre long bridge in 2 minutes. The length of the train is half that of the bridge. What is the speed of the train? a) 45 Km/h b) 30 Km/h c) 50 Km/h d) 44 Km/h. Answer : a) 45 Km/h Solution : length of the bridge = 1000m Length of the train = 500m Distance travelled in 2 min = 1500m Speed = 1500 x 60 / 2 m/hr = 45 km/ hr 14. A train, traveling at 48 Km/h, takes one minute to pass a telegraph pole. What is the length of the train in metres? a) 80 b) 320 c) 800 d) 1000 Answer : c) 800 Solution : length of the train = distance travelled in 1 min = 48 x 1000 / 60 = 800m 15. A man can row 1 Km against the current of a river in 6 minutes and with the current in 5 minutes. What is the speed of the river (in Km/h)? a) ½ b) 1 c) 11 d) 22 Answer : b) 1 Solution : b-s= 1/6 km /min = 10 m/ hr b + s = 1/5 km /min = 12 km/ hr s = 12- 10 / 2 = 1 km /hr
16. A train 750 metres long takes 70 seconds to completely pass a railway platform of 1 Km long. What is the speed of the train in Km/h? a) 100 b) 90 c) 75 d) 60 Answer : b) 90 Solution : distance travelled = 1750m Speed = 1750 / 70 m /sec = 1750 x 18 / 70 x 5 km/hr
=90 km /hr 17. Two trains are traveling towards one another, on parallel tracks, at speeds of 68 and 76 Km/h respectively. If the two trains are respectively 800 and 880 m long, how many seconds will elapse before they are completely clear from one another? a) 36 secs b) 45 secs c) 30 secs d) 42 secs Answer : d) 42 secs Solution : Distance travelled = 800+ 880 =1680m Speed = 68 + 76 = 144 km /hr
= 144 x 5 / 18 m/sec Time taken = 1680 x 18 / 144 x 5 = 42 sec
18. A man can row 9 Km an hour in still water, if he takes twice as long to row up as to row down a river. What is the rate of flow of the river? a) 1 Km/h b) 1.5 Km/h c) 3 Km/h d) 6 Km/h Answer : c) 3 Km/h Solution : upstream time : downstream time = 2:1 Upstream velocity : downstream velocity = 1: 2 b-s : b+s = 1:2 9-s : 9+s = 1:2 18 – 2s = 9 +s 3s = 9 S=3
19. A trains 125 metres long is traveling at the speed of 36 Km/h. In how many seconds would it cross a platform 375 metres long? a) 62.5 b) 50 c) 75 d) 37.5 Answer : b) 50
Solution : Distance travelled = 125 + 375 = 500m Speed = 36 km /hr
= 36 x 5 / 18 m/sec = 10 m/sec Time taken = 500 /10 = 50 sec
20. A 300 meter long train crosses an electric pole in 15 seconds. In how many seconds will it cross a bridge 0.6 Km long? a) 50 sec b) 45 sec c) 42 sec d) 60 sec Answer : b) 45 sec Solution : Time taken to cover 300m = 15sec Time taken to cover 300 +600 m = 15 x900 / 300 = 45s 21. A 200 metre long train crosses another one traveling in opposite direction in 15 seconds, if the length of the other train is 300 metres and the speeds of both the trains are equal. Find the speed of the train. a) 30 Km/h b) 54 Km/h c) 60 Km/h d) 90 Km/h Answer : c) 60 Km/h Solution : distance travelled = 200 + 300 = 500m If v is the speed relative speed = 2v 500 / 2v = 15 V= 500 / 30 m /s = (500 / 30 ) ( 18/5) km/hr =60km/hr 22. A 300 metre long train, running at a speed of 54 Km/h crosses a bridge in 1 minute. In how many seconds would it cross a platform which is twice the length of the bridge? a) 150 b) 120 c) 80 d) 100
Answer : d) 100
Solution : speed = 54 km/h = 54 x 5 / 18 m/ s = 15 m/s (300 + d) / 15 = 60 20 + (d /15 ) = 60 d/15 = 40 20 + (2d / 15 ) = 20 +80 = 100s 23. A train 280 m long running with speed of 63 Km/h will pass an electric pole in a) 20 sec b) 16 sec c) 15 sec d) 18 sec Answer : b) 16 sec Solution : speed = 63km/h = 63x 5 /18 m/s Time taken = 280 x 18 / 63 x 5 = 16s 24. A train 120m long crosses a standing man in 15 seconds. The speed of the train is : a) 32 Km/h b) 36.5 Km/h c) 28.8 Km/h d) 40 Km/h Answer : c) 28.8 Km/h Solution : speed =distance / time = 120/15 m/s = 8 x 18 / 5 km/h = 28.8 km/h 25. A train 60 m long passes a platform 90 m long in 10 seconds. The speed of the train is : a) 10 Km/h b) 15 Km/h c) 54 Km/h d) 48 K Answer : c) 54 Km/h Solution : Distance travelled = 60 + 90 = 150m Speed= distance /time = 150 / 10 m/s = 15 x 18 /5 km/h = 54 km/h 26. A train 110 m long is traveling at a speed of 58 Km/h. The time in which it will pass a passer by walking at 4 Km/h in the same direction is: a) 6 secs b) 7½ secs c) 7
1 3
secs d) 7
1 3
min.
Answer : c) 7
1 3
secs
Solution : Distance travelled =110 m Relative velocity = 58 -4 =54km/h =54 x 5 /18 = 15m/s Time taken = 110/15 = 7 1/3 s 27. If a man can swim downstream at 6 Km/h and upstream at 2 Km/h. His speed in still water is : a) 4 Km/h b) 2 Km/h c) 3 Km/h d) 2.5 Km/h Answer : a) 4 Km/h Solution : m + s= 6 m-s= 2 m = 6+2 /2 = 4 28. A man rows 750 m in 675 seconds against the stream and returns in 7½ minutes. His rowing speed in still water is: a) 3 Km/h b) 4 Km/h c) 5 Km/h d) 6 Km/h Answer : c) 5 Km/h Solution : 750 / b-s = 675 750 / b + s = 450 b - s = 750 / 675 b + s = 750 /450 b= 25/18 m/ s = 25/18 ( 18/5) km / h = 5 km / h
29.
A man can row 9
1 3
Km/h in still water and find that it takes him thrice as much time to
row up than as to row down the same distance in the river. The speed of the current is:
a) 3
1 3
Km/h
Answer : c) 4
2 3
b) 3
1 9
Km/h
c) 4
2 3
Km/h
d) 14 Km/h
Km/h
Solution : b= 28 /3 km/h Upstream time : downstream time = 3:1 Upstream velocity : downstream velocity = 1:3 28/3 – s = 28/3 +s = 1;3 4s = 2x 28 /3 S= 14/3 = 4
2 3
Km/h
30. If a man’s rate with the current is 11 Km/h and the rate of the current is 1.5 Km/h, then the man’s rate against the current is : a) 8 Km/h b) 9.5 Km/h c) 9 Km/h d) 6.25 Km/h Answer : b) 9.5 Km/h Solution : b+s = 11km/h S= 1.5 km/h b = 9.5km/h 31.
River is running at 2 Km/h. It takes a man thrice as long to row up as to row down the river. The rate of the man in still water is : a) 6 Km/h b) 4 Km/h c) 10 Km/h d) 8 Km/h Answer : b) 4 Km/h
Solution : s= 2 km/h b + s : b – s = 3:1 3b -6 = b+2 2b= 8
B=4km/h 32.Bombay express left Delhi for Bombay at 14.30hr, traveling at a speed of 60 Kmph and Rajdhani express left Delhi for Bombay on the same day at 16.30 hrs, traveling at a speed of 80 Kmph. If the distance between Bombay and Delhi is 680 Kms, how far away from Delhi will the two trains meet? a) 120 Km b) 360 Km c) 480 Km d) 500 Km Answer : b) 360 Km Solution : After 2 hours at 16.30, distance between the trains = 680 - 120 = 560 km Relative velocity = 140 km/h Time taken to cover 560 km = 4 hr Distance from delhi = 60( 2+40 = 360km 33.A man drives 150 Km from A to B in 3 hours 20 min and returns to A in 4 hours 10 min. Then average speed from A to B exceed the average speed for entire trip by a) 5 Km/h b) 4.5 Km/h c) 4 Km/h d) 2.5 Km/h Answer : a) 5 Km/h Solution : Average speed from A to B= 150 / 3 1/3 = 45 km/h Average speed for entire trip = 300 / 7 ½ = 40 km/h Difference = 5 km/h
34.A train traveling at a speed of 90 Kmph, crosses a pole in 10 second. The length of the train is a) 250 m b) 150 m c) 900 m d) 100 m Answer : a) 250 m Solution : sped = 90 km/h = 90 (5/18 ) m/s = 25 m/s Distance travelled in 10s = 250 m
35.A train crosses a platform 100m long in 60 seconds at a speed of 45 Kmph. The time taken by the train to cross an electric pole is a) 8 sec b) 52 sec c) 1 minute d) data inadequate Answer : b) 52 sec Solution : speed = 45 km/h = 45 x 5 /18 m/s = 25/2 m/s Time taken to cover 100 m = 100 x 2 / 25 = 8s Time taken to cross the pole = 60 -8 =52 s 36.A train 150m long moving at a speed of 25 m/sec overtaks a man moving at 5 m/sec in opposite direction. The train will pass the man in a) 5 sec
b) 6 sec
c) 4
2 7
sec
d) 8 sec
Answer : a) 5 sec Solution : Relative velocity = 25 + 5 =30 m/s Time taken to cover 150 m = 150 /30 s =5 s 37.Two trains 200m and 150m long are running on parallel rails at the rate of 40 Kmph and 45 Kmph respectively. In how much time will they cross each other, if they are running in the same direction. a) 72 sec b) 132 sec c) 192 sec d) 252 sec Answer : d) 252 sec
Solution : Relative velocity = 45 -40 =5 km/h = 5 x 5 /18 m/s Time taken to cross = time taken to cover 200 + 150 = 350 m =350 x 18 / 5x 5 = 252 s
38.Two trains are moving in the same direction at 65 Kmph and 45 Kmph. The faster train crosses a man in slower train in 18 seconds. The length of the faster train is a) 120 m b) 180 m c) 100 m d) 145 m Answer : c) 100 m Solution :
Relative velocity = 65 – 45 = 20 km /h = 20 x 5 / 18 m/s Length of the faster train =distance travelled to 18s = 100m 39.A train overtakes two persons who are walking in the same direction in which the train is going at the rate of 2 Kmph and 4 Kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is a) 72 m b) 54 m c) 50 m d) 45 m Answer : c) 50 m Solution : s be the speed of the train and l be the length of the train Relative velocity with respect to slow person = s – 2 x 5 /18 m/s Relative velocity with respect to fast person = s – 4 x 5 /18 m/s l /( s – 10/18) =9
; l / ( s – 20/18) =10
l = 10 ( s – 10/9) =10( s – 5/9 – 5/9 ) =10 (l/9 – 5/9) 9l = 10l – 50 L= 50 m
40.A 150 m long train passes a stone in 15 seconds and another train of the same length traveling on opposite direction in 8 seconds. The speed of the second train is a) 60 Km/h b) 72 Km/h c) 66 Km/h d) 99 Km/h Answer : d) 99 Km/h
Solution : s1 = speed of the first train = 150 /15 = 10 m/s S2 = speed of the second train 300 / s1 + S2 = 8 300 /10
+ S2
=8
80 + 8 S2 = 300
S2 = 220 /8 m/s = 220 x 18 / 8 x 5 km/h =99 km /h
41.A man can row a boat at 10 Kmph on still water. If the speed of the stream is 6 Kmph, the time taken to row a distance of 80 Km down the stream is a) 8 hours b) 5 hours c) 10 hours d) 20 hours Answer : b) 5 hours Solution : b= 10 km/h S= 6 km/h Speed down the stream = 16 km/h Time taken to cover 80 km = 80 / 16 = 5 hr 42.A boat covers 24 Km upstream and 36 Km downstream in 6 hours which it covers 36 Km upstream and 24 Km downstream in 6½ hours. The velocity of the current is a) 1 Km/h b) 1.5 Km/h c) 2 Km/h d) 2.5 Km/h Answer : c) 2 Km/h Solution : 24 / b-s + 36/ b + s =6 4x + 6y = 1……………………..(1) 24 / b+s + 36/ b - s = 6 ½ 72x + 48 y = 13 …………………(2) (2) – 8(1) => 40x =5 X= 1/8 b-s = 8 by (1) 6y= ½ y=1/12 b+s= 12 2s= 4
S=2
43.If a man rows at a rate of 5 Kmph in still water and his rate against the current is 3.5 Kmph, then the man’s rate along the current is a) 4.25 Km/h b) 6 Km/h c) 6.5 Km/h d) 8.5 Km/h Answer : c) 6.5 Km/h
Solution : b= 5 km/h b- s = 3.5km/h s= 1.5 km/h b + s = 6.5 km /hr 44. A train covers a certain distance in 50 minutes, if it runs at a speed of 48 Kmph on an average. The speed at which the train must run to reduce the time of journey to 40 minutes will be a) 50 Km/h b) 55 Km/h c) 60 Km/h d) 70 Km/h Answer : c) 60 Km/h Solution : time =distance /speed d/48 = 5/6 => d=40km speed = distance /time = 40 / (4/6) = 60km note : 50 min = 5/6 hr 45. A man covers a certain distance on scooter. Had he moved 3 Km/h faster he would have taken 40 minutes less. If he had moved 2 Kmph slower he would have taken 40 minutes more. Find the distance (in Km) a) 20 b) 36 c) 37.5 d) 40 Answer : d) 40 Solution :
d/s - d/s+3 = 2/3
3d / s(s+3) = 2/3 2s(s+3) = 9d…………..(1)
d/s-2 - d/s =2/3 2d /s(s-2) = 2/3 2s(s-2) = 6d…………..(2) (1) /(2) =>
s+3/ s-2 =3/2
2s+6 = 3s-6 S=12 D=2 x 12 x 10 /6 =40km 46) A and B run a ½ km race, their speeds being in the ratio 5:4. How much start in terms of distance should A give B so that they both finish the race simultaneously? a) 80 m b) 100m c) 120m d) 140m Answer : b)100m Solution : ratio of speeds is 5:4 Ratio of distance is 500 : 400 When A covers ½ km , B covers only 400m A should give B , a start of 100m to finish simultaneously. 47) A takes 3mins 45secs to complete a km. B takes 4mins to complete the same 1km track. If A and B are to participate in a race of 2 kms, how much start must give in terms of distance so that they both finish the race simultaneously? a)62.5m b)120m c) 125m d) 130m Answer : c) 125m Solution : Time difference in 1 km run = 15 secs Time difference in 2 km run = 30 secs Distance travelled by B in 30 secs = 1000/4( 30/60) = 125 48 ) In a 100m race , A runs at 8kmph. If Agivees B a start o 4m and still beats him by 15 secs , what is the speed of B ? a) 5kmph b) 5.5kmph c) 5.76kmph d) 6kmph Answer : c) 5.76kmph Solution : time taken by A = (100/8000) x 60 x 60 = 45 secs B covers 100-4 =96m in 45 +15 secs Speed of B = 96/60 m/s
= ( 8/5 ) ( 18 / 5) km/h= 32 x 18 / 100 = 5.76 49 ) A , B and C are three contestants in a 1kmrace. If A can give B a start of 40m, and Acan give C a start of 64m , how many meters start can B give C? a) 25m b) 20m c) 30m d0 35m Answer : a) 25m Solution : When A covers 1000m, B covers 960m When A covers 1000m, C covers 936m When B covers 1000m, C covers 936/ 960 (1000) m= 975m B can give a start of 1000- 975 = 25m 50) In a 100m race, A can beat B by 25m and B can beat c by 4m. in the same race , A can beat C by a)21m b)26m c)28m d029m answer : c) 28m Solution : When A covers 100m, B covers 75m When B covers 100m, C covers 96m
When B covers 75m, C covers 96/100 ( 75) m = 72 A can beat C by 100 – 72 = 28 m 51) Two friends M and N start from the same point at the same time and run in the same direction on a circular track of 352m long. If their speeds are 8 m/s and 11m/s when will they meet again at the starting point? a) 352s b) 32s c) 44s d)none ans : a)352s solution : time taken for 1 full round are 352/ 8 = 44s 352/11 = 32s Lcm = 4 x 11 x8 = 352s
52) A and B run on a circular track of length 600m with a speed of 5km/h and 2 km/h. they start from the same place at the same time and same direction. When will they be together again for the first time ? a) 700s
b) 710s
c) 720s
d) 800s
Ans: c) 720s Solution : relative speed = 5-2 = 3km/h 3 x (5/18) = 5/6 m/s They will be together for the first time after 600/ ( 5/6) = 720s 53) three friends Ram and Robert run along a circular track of 500m length with a speed of 8km/h. 5km/h, and 3km/h respectively. When will they all be together again for the first time? a)20min b) 25min c) 30min d)35min ans :c) 30min solution : ram is fastest runner ram will meet robert after 500/ (8-5) (5/18) =600s =10m ram will meet rahim after 500/ (8-3) (5/18) =360s =6m lcm of 10,6 is 30 T hey all will meet again for the first time after 30 min
