SSC CGL Mains 20241)On a 2200 m long circular track, Sarita and Kavita drove their cycles from the same point but in opposite direction with the speeds 20 km/hr and 16 km/hr, respectively. After how much time will they meet again for the first time?
3 minutes 40 seconds
SSC CGL 20222)A policeman spotted a thief 40 metres ahead of him. The moment they both saw each other they started running in the same direction on the same track. The thief was running at 10 m/sec and the policeman was chasing him at the speed of 12 m/sec. How much distance (in metres) the policeman needed to cover to catch the thief?
240
SSC CGL 20223)Ram starts from point A at 8 a.m. and reaches point B at 2 p.m. on the same day. On the same day, Raju starts from point B at 8 a.m. and reaches point A at 6 p.m. on the same day. Both points A and B are separated by only a straight line track. At what time they both meet?
11:45 a.m.
, Avg: 03:01 , 100%✓ SSC CGL 20224)A boat covers a certain distance against the stream in 9 hours 36 min and it covers the same distance along the stream in 6 hours. What is the ratio of the speed of the boat in still water to that of the stream?
13 ∶ 3
SSC CGL 20225)Train A running at 81 km/h takes 72 sec to overtake train B, when both the trains are running in the same direction, but it takes 36 sec to cross each other if the trains are running in the opposite direction. If the length of train B is 600 metres, then find the length of train A. (in metres)
480
, Avg: 01:46 , 75%✓ SSC CGL 20226)Two stations R and S are 400 km apart from each other. A train leaves from R to S and simultaneously another train leaves from S to R. Both trains meet after 10 hours. If the speed of the first train is 4 km/hr more than the second train, then what is the speed of the slower train?
18 km/hr
SSC CGL 20227)A swimmer swims from a point P against the current for 6 min and then swims back along the current for next 6 min and reaches at a point Q. If the distance between P and Q is 120 m then the speed of the current (in km/h) is:
0.6
, Avg: 00:13 , 50%✓ SSC CGL 20228)A man rows a boat a certain distance downstream in 9 hours, while it takes 18 hours to row the same distance upstream. How many hours will it take him to row three-fifth of the same distance in still water?
7.2
, Avg: 00:22 , 31%✓9)Two objects are moving on a circular path of length 160 km at a speed of 30 kmph and 50 kmph in the opposite direction. At how many point will both the objects meet on a circular path if they are continuously moving?
10)Two objects are moving on a circular path of length 600 m at a speed of 20 m/sec and 50 m/sec in the same direction. At how many point will both the objects meet on a circular path if they are continuously moving?
11)A tiger is 50 of its own heaps behind a deer. The tiger takes 5 heaps per minute to the deer’s 4. If the tiger & the deer cover 8 m & 5 m per heap respectively. What distance will the tiger have to run before it catches the deer?
12)Two superfast trains P & Q start from station A & B towards B & A respectively. After passing each other, they take 4 hours 48 mins & 3 hours 20 min to reach B & A respectively. If the train P is moving at 45 kmph. Find the speed of the train Q.
13)A hunter fires two shots from the branch of a tree at an interval of 76 secs. A tiger separating too fast hears the two shots at an interval of 83 secs. If the velocity of the sound is 1195.2 kmph, then find the speed of the tiger?
14)Two bullets were fired at a place at an interval of 28 min 30 sec. A person approaching the firing point in his car hears the two sounds at an interval of 27 mins. The speed of sound is 330 m/s. What is the speed of car?
15)A boat covers 12 km upstream & 18 km downstream in 3 hrs, while it covers 36 km upstream & 24 km downstream in 6.5 hrs. What is the speed of the current?
16)A train leaves Amritsar at 6 am & reaches Delhi at 12 noon. Another train leaves Delhi at 8 am & reaches Amritsar at 5 pm. At what time do the two trains cross each other?
, Avg: 02:04 , 100%✓ SSC CGL 202217)Two trains are running on parallel tracks in the same direction at the speed of 80 km/h and 90 km/h, respectively. The trains crossed each other in 3 minutes. If the length of one train is 230 m, then what is the length (in m) of the other train?
270
, Avg: 00:30 , 85%✓ SSC CGL 202218)A 240-m long train crosses a 360-m long tunnel in 30 seconds. What is the speed of the train (in km/h)?
72
, Avg: 02:03 , 75%✓ SSC CGL 202219)The distance between two stations A and B is 200 km. A train runs from A to B at a speed of 75 km/h, while another train runs from B to A at a speed of 85 km/h. What will be the distance between the two trains (in km) 3 minutes before they meet?
8
, Avg: 00:54 , 66%✓ SSC CGL 202220)Anup can row 33 km downstream and 35 km upstream in 8 hours. He can also row 44 km downstream and 28 km upstream in the same time. How much time (in hours) will he take to row 55 km downstream and 14 km upstream?
7
, Avg: 01:03 , 40%✓ SSC CGL 202221)A railway engine passes two bridges of lengths 400 m and 235 m in 100 seconds and 60 seconds, respectively. Twice the length of the railway engine (in m) is:
25
, Avg: 01:29 , 100%✓ SSC CGL 202222)A boat can cover a distance of 56 km downstream in 3.5 hours. The ratio of the boat in still water and the speed of stream is 3 : 1. How much time (in hours) will the boat take to cover a distance of 41.6 km downstream?
2.6
, Avg: 01:15 , 71%✓ SSC CGL 202223)A and B started their journeys from X to Y and Y to X, respectively. After crossing each other, A and B completed remaining parts of their journeys in 6\({1 \over 8} \) hours and 8 hours, respectively. If the speed of A is 32 km/h, then the speed, in km/h of B is:
28
, Avg: 00:57 , 66%✓ SSC CGL 202224)A boatman can row his boat in still water at a speed of 9 km/h. He can also row 44 km downstream and 35 km upstream in 9 hours. How much time (in hours) will he take to row 33 km downstream and 28 km upstream?
7
, Avg: 02:11 , 61%✓ SSC CGL 202225)A motorboat whose speed is 20 km/h in still water takes 30 minutes more to go 24 km upstream than to cover the same distance downstream. If the speed of the boat in still water is increased by 2 km/h, then how much time will it take to go 39 km downstream and 30 km upstream?
SSC CPO 202026)The speed of a boat in still water is 15 km/h, and the speed of the current is 5 km/h. In how much time (in hours) will the boat travel a distance of 60 km upstream and the same distance downstream?
9
SSC CPO 202027)A train x running at 74 km/h crosses another train y running at 52 km/h in the opposite direction in 12 seconds. If the length of y is two-thirds that of x, then what is the length of y (in m) ?
168
SSC CPO 202028)A train travelling at the speed of x km/h crossed a 300 m long platform in 30 seconds, and overtook a man walking in the same direction at 6 km/h in 20 seconds. What is the value of x?
96
, Avg: 00:46 , 50%✓ SSC CPO 202029)A train x running at 74 km/h crosses another train y running at 52 km/h in the opposite direction in 12 seconds. If the length of y is two-thirds that of x, then what is the length of x (in m)?
252
SSC Selection Post Matric 202230)A 200 m long train crosses a pole in 10 seconds. Another train of length 250 m crosses a platform which is 200 m long in 15 seconds. If both trains move in opposite directions, how much time (in seconds) will they take to cross each other completely?
9
, Avg: 00:58 , 100%✓ SSC Selection Post Matric 202231)The distance between two persons A and B is 432 km. They started travelling towards each other at 7 : 20 hours at 24.5 km/h and 20.5 km/h. respectively. At what time did they meet?
16:56 hours
SSC Selection Post Matric 202232)The time taken by a boat to go a certain distance upstream is twice the time taken by it to go the same distance downstream. If the speed of the stream is 3 km/h, then how much time (in hours) will the boat take to go 52 km upstream?
SSC Selection Post Matric 202233)How long (in seconds) will a train of a length 450 m, running at a speed of 69 km/h, take to cross a man moving in the opposite direction at a speed of 3 km/h?
22.5
, Avg: 01:16 , 66%✓ SSC Selection Post Matric 202234)The speed of a boat in still water is 25 km/h. It takes \(33\frac{1}{3}\) % more time to cover a certain distance in still water than to cover the same distance downstream. How much time (in hours) will the boat take to go 75 km downstream?
, Avg: 00:24 , 100%✓ SSC Selection Post Matric 202235)The speed of a boat in still water is 15 km/h and the speed of the stream is 3 km/h. How much time (in hours) will be boat take if it goes 36 km downstream?
2
SSC Selection Post Matric 202236)A 280 m long train is running at a speed of 54 kmph. In how much time (in seconds) will it cross a man moving at 12 kmph in the same direction as that of the train?
24
, Avg: 01:33 , 100%✓ SSC Selection Post Matric 202237)Two trains start at the same time from two stations and proceed towards each other at speeds 88 km/h and 75 km/h, respectively. When they meet, it is found that one train has travelled 65 km more than the other. What is the distance(in km) between the two stations?
815
, Avg: 02:21 , 71%✓ SSC CHSL 202138)A train, 500 m long, passes a railway platform 400 m long, in one minute with uniform speed. What is the time (in seconds) taken by the train to pass a man riding a motorbike, travelling opposite to the direction of the train, at a speed of 18 km/h?
25
, Avg: 01:25 , 50%✓ SSC CHSL 202139)A boat can go 15 km downstream and 8 km upstream in 2 h. It can go 20 km downstream and 12 km upstream in 2 h 50 min. What is the speed (in km/h ) of the boat while going downstream?
15
, Avg: 02:56 , 50%✓ SSC CHSL 202140)Ajit Singh left from place P at 9.30 a.m. for place Q, and David Raj left place Q at 1.30 p.m. for place P. The distance between them is 416 km. If Ajit Singh’s speed is 44 km/h and David Raj’s speed is 52 km/h, then at what time will they meet each other?
, Avg: 00:59 , 50%✓ SSC CHSL 202141)Sunil can row a boat 20 km upstream in 1 hour 15 minutes. If the speed of the current of the river is 2 km/h, then how much time will he take to row the boat 30 km downstream?
1 h 30 m
, Avg: 01:59 , 75%✓ SSC CHSL 202142)Two trains X and Y of lengths 450 meters and 550 meters, respectively, are running in the same direction on parallel tracks. If the speeds of X and Y are 58 km/h and 86 km/h, respectively, then what will be the time taken by then to cross each other?
(correct to one decimal place)
128.6 seconds
, Avg: 01:03 , 88%✓ SSC CHSL 202143)Ravi can row a boat in still water at the speed of 14 km/h. If a river is flowing at the sped of 2 km/h and Ravi takes 3 hours to cover a certain distance upstream, then how much time will he take to cover the same distance downstream?
2 h 15 m
, Avg: 02:14 , 50%✓ SSC CHSL 202144)The speed of a train is 78 km/h. It crosses a tunnel in 45 s and overtakes a person walking at a speed of 6 km/h, in the same direction, in 15 s. The length (in m) of the tunnel is:
675
, Avg: 01:02 , 100%✓ SSC CHSL 202145)A train starts running at a uniform speed of 60 km/h from station P towards station Q. At the same time another train starts running from station Q towards station P. If the distance between the stations P and Q is 275 km and the trains meet in two and a half hours, then what is the speed of the train running towards station P in km/h?
50
, Avg: 00:51 , 60%✓ SSC CHSL 202146)A boat can travel with a speed of 19 km/h in still water. If the speed of the stream is 3 km/h, then what will be the total time (in hours) taken by the boat to go 88 km downstream and 24 km upstream?
5.5
, Avg: 01:05 , 85%✓ SSC CHSL 202147)Trains A and B of lengths 329 m and 296 m, respectively, are running in opposite directions on parallel tracks, at the speeds of 85 km/h and 65 km/h, respectively. In what time (in seconds) will they cross each other?
15
, Avg: 01:33 , 83%✓ SSC CHSL 202148)Two cars X and Y start running towards each other from two places 216 km apart. The ratio of the speeds of X and Y is 5 ∶ 7 and the speed of X is 60 km/h. After how many minutes will X and Y meet each other?
90
, Avg: 01:37 , 50%✓ SSC CHSL 202149)Two person P and Q are 844 m apart. They both start cycling simultaneously in the same direction with speeds of 12 m/s and 8 m/s, respectively, In how much time will P overtake Q?
, Avg: 02:19 , 50%✓ SSC CHSL 202150)The speed of a boat in downstream is 150% more than its speed in upstream. If the time taken by the boat for going 80 km downstream and 50 km upstream is 8.2 hours, then what is the speed (in km/h) of the boat in downstream?
, Avg: 01:00 , 100%✓ SSC CHSL 202151)Two trains start at the same time from two stations and proceed towards each other at speeds of 90 km/h and 70 km/h, respectively. When they meet, it is found that one train has travelled 140 km more than the other. What is the distance (in km) between the two stations?
1120
, Avg: 00:42 , 20%✓ SSC CGL 202052)A boat can go 3.6 km upstream and 5.4 km downstream in 54 minutes, while it can go 5.4 km upstream and 3.6 km downstream in 58.5 minutes. The time (in minutes) taken by the boat in going 10 km downstream is :
50
Let speed of boat in still water be x kmph and speed of stream be y kmph.
\({3.6\over x-y}+{5.4\over x+y}={54\over60}\) ; Again, \({5.4\over x-y}+{3.6\over x+y}={58.5\over60}\) ; ⇒ x + y = 12 kmph ;
Required time = \({10\over12}\times 60 = 50 \space minutes\)
, Avg: 01:19 , 75%✓ SSC CGL 202053)The distance between two stations, A and B, is 428 km.A train starts from station ‘A’ at 6:00 a.m. and moves towards station ‘B’ at an average speed of 48 km/h. Another train starts from station ‘B’ at 6:20 a.m. and moves towards station ‘A’ at an average speed of 55 km/h. At what time will the trains meet?
10 : 20 a.m.
Distance travelled by train in 20 min = \(48\times{20\over60}\) = 16 km. ; Now when both train starts moving the distance between them is = 428 - 16 = 412 km. ;
Relative speed = 55 + 48 = 103 km/ hr ; Time = \(412\over103\) = 4 hr. ; Hence both train will meet at 6:20 + 4 = 10:20 am
, Avg: 01:28 , 66%✓ SSC CGL 202054)A train crosses a platform 180 m long in 60 sec at a speed of 72 km/h. The time taken by the train to cross an electric pole is:
51 seconds
Length of platform = 180 m;
Time = 60 sec;
Speed = 72 km/hr = \(72\times 5\over18\) = 20 metre/second;
Total length = length of platform + length of train = 180 + length of train;
Speed = length/time;
180 + length of train = \(20 \times60\);
Length of train =1200 - 180 = 1020 m;
The time taken by the train to cross an electric pole = 1020/20 = 51 seconds
, Avg: 01:00 , 66%✓ SSC CGL 202055)Two cars A and B leave Delhi at 8:30 a.m. and at 9 a.m. for Shimla, respectively. They travel at the speeds of 40km/h and 50 km/h respectively. How many kilometres away from Delhi will the two cars be together?
100 km
Cars A and B leave Delhi at 8:30 a.m. and at 9 a.m. for Shimla, respectively so, Distance traveled by car A in 30 min = \(speed \times times = 40 \times 1/2 \) = 20 km;
(30 min = 30/60 hr = 1/2 hr)
Relative speed of car B = 50 - 40 = 10 km/hr;
Time taken by car B to cover 20 km = 20/10 = 2 hr;
(Time = distance/speed)
Distance covered in 2 hr = 50 \times 2 = 100 km
, Avg: 01:00 , 75%✓ SSC CGL 202056)The two trains leave Varanasi for Lucknow at 11:00 a.m. and at 11:30 a.m., respectively and travel at speeds of 110 km/h and 140 km/h, respectively. How many kilometers from Varanasi will both trains meet?
\(256{2\over3}\)km
Let the train which leaves Varanasi at 11:00 be A and another train be B.
Speed of train A = 110 km/hr;
Speed of train B = 140 km/hr;
Distance covered by train A in 30 min(30/60 = 1/2 hr) = speed x time = 110 x 1/2 = 55 km;
At 11:30, distance between both trains will be 55 km.
Relative speed of train B = 140 - 110 = 30 km/hr;
Time taken by train B to meet = 55/30 = 11/6 hr;
Distance covered by train B in 11/6 hr = 140 x 11/6 = \(256{2\over3}\)km
, Avg: 01:43 , 54%✓ SSC CGL 202057)In a stream running at 3 km/h, a motorboat goes 12 km upstream and back to the starting point in 60 minutes. Find the speed of the motorboat in still water. (in km/h)
\(3(4+\sqrt{17})\)
Speed of stream = 3 km/hr;
Let the speed of motor boat be v.
Relative speed in upstream = v - 3 km/hr;
Relative speed in upstream = v + 3 km/hr;
Distance = 12 km;
Time = 60 min = 1 hr;
Time = Distance/speed;
\({12\over v-3}+{12\over v+3} =1\);
12(v + 3) + 12(v - 3) = (v + 3)(v - 3);
24v = \(v^2-3^2\);
\(v^2 − 24v − 9 = 0\);
From Dharacharya Formula, \(x= {-b\pm\sqrt{b^2-4ac}\over2a}\); \(x= {-(-24)\pm\sqrt{(-24)^2-4\times1(-9)}\over2}\); \(x = {24\pm6\sqrt{17}\over2}\); As x cannot be negative \(x ={ 6(4+\sqrt{17})\over2} = 3(4+\sqrt{17})\)kmph.
SSC CGL 202058)The distance between two stations A and B is 575 km. A train starts from station ‘A’ at 3:00 p.m. and moves towards station ‘B’ at an average speed of 50 km/h. Another train starts from station ‘B’ at 3:30 p.m. and moves towards station ‘A’ at an average speed of 60 km/h. How far from station ‘A’ will the trains meet ?
275 km
Distance between stations = 575 km;
Speed of train A = 50 km/hr;
Distance covered by train A in (30 min = 1/2 hr) =\( time \times speed = 50 \times 1/2 = 25 km\);
Trains are running in opposite direction so,
Relative speed = 50 + 60 = 110 km/hr;
Distance covered by both train = 575 - 25 = 550 km;
Time taken by both trains to meet = 550/110 = 5 hr;
Distance covered by train A in 5 hr =\( 5 \times 50 \)= 250 km;
Distance covered by train A from station A = distance covered by train A in 30 min + distance covered by train A in 5 = 250 + 25 = 275km
, 50%✓ SSC CGL 202059)A train X travelling at 60 km/h overtakes another train Y, 225 m long, and completely passes it in 72 seconds. If the trains had been going in opposite directions, they would have passed each other in 18 seconds. The length (in m) of X and the speed (in kmph) of Y are, respectively :
255 and 36
Time taken to cross in same direction = 72 second;
Time taken to cross in opposite direction = 18 second;
Speed of train X = 60 km/hr =\( 60 \frac{5}{18}\) = 16.66 m/sec;
Length of train Y = 225 m;
Let the length of train X be l m and speed of train Y be x m/sec.
Total length = (225 + l) m;
Relative speed when trains run opposite direction = (16.66 + x) m/sec;
Length = speed x time;
225 + l = (16.66 + x) x 18;
225 + l = 300 + 18x;
l = 75 + 18x ---(1);
Relative speed when trains run opposite direction = (16.66 - x) m/sec;
225 + l = (16.66 - x) 72;
225 + l = 1200 - 72x;
l = 975 - 72x ---(2);
By eq(1) and (2),
75 + 18x = 975 - 72x;
90x = 900;
x = 10 m/sec;
Speed (in km/h) of Y = \(10 \frac{18}{5}\) = 36 km/hr;
Put the value of x in eq(1);
l = 75 + 18 10 = 255 m.
, Avg: 00:45 , 100%✓ SSC CGL 201960)Places A and B are 396 km apart. Train X leaves from A for B and train Y leaves from B for A at the same time on the same day on parallel tracks. Both trains meet after \(5\frac{1}{2}\) hours. The speed of train Y is 10 km/h more than that of train X. What is the speed (in km/h) of train Y?
, Avg: 01:16 , 100%✓ SSC CGL 201961)Renu was sitting inside train A, which was travelling at 50 km/h. Another train, B, whose length was three times the length of A crossed her in the opposite direction in 15 seconds. If the speed of train B was 58 km/h, then the length of train A (in m) is:
, Avg: 01:40 , 100%✓ SSC CGL 201962)The speed of a boat in still water is 18 km/h and the speed of the current is 6 km/h. In how much time (in hours) will the boat travel a distance of 90 km upstream and the same distance downstream?
SSC CGL 201963)A man can row a distance of 900 metres against the stream in 12 minutes and returns to the starting point in 9 minutes. What is the speed (in km/h) of the man in still water?
\(5\frac{1}{4}\)
, Avg: 00:45 , 61%✓ SSC CGL 201964)A and B started their journeys from X to Y and Y to X, respectively. After crossing each other, A and B completed the remaining parts of their journeys in \( 6\frac{1}{8}\) hours and 8 hours respectively. If the speed of B is 28 km/h, then the speed (in km/h) of A is:
32
By the formula,
Ratio of the speed =\( \sqrt{\ inverse\ \ ratio\ \ of\ \ the time}\);
\(\frac{S_a}{S_b} = \sqrt{\frac{t_b}{t_a}};\)
\(S_b = 28 km/hr;\)
\(t_a \)= \(6\frac{1}{8} = \frac{49}{8};\)
\(t_b \)= 8;
\(\Rightarrow \frac{S_a}{28} = \sqrt{\frac{8}{\frac{49}{8}}};\)
\(\Rightarrow \frac{S_a}{28} = \sqrt{\frac{64}{49}};\)
\(\Rightarrow \frac{S_a}{28} = \frac{8}{7};\)
\(S_a = 32 km/hr\)
SSC CGL 201965)A train travelling at the speed of x km/h crossed a 200 m long platform in 30 seconds and overtook a man walking in the same direction at the speed of 6 km/h in 20 seconds. What is the value of x ?
60
Length the length off the traiin be l m.
A train travelling at the speed of x km/h crossed a 200 m long platform in 30 seconds;
So, length = speed \times time;
(l + 200) = 30x;
l = 30x - 200 ---(1);
Speed of man = 6 km/hr = \(6 \times \frac{5}{18} \)= 5/3 m/sec;
Relative speed = x - 5/3;
\(\frac{l}{20} = \frac{3x - 5}{3};\)
put the value of l,
\(\frac{30x - 200}{20} = \frac{3x - 5}{3}; 90x - 600 = 60x - 100;\)
30x = 500;
x = 50/3 m/sec = \(\frac{50}{3} \times \frac{18}{5} \)= 60 km/hr
, Avg: 01:14 , 60%✓ SSC CGL 201966)Abhi rows upstream a distance of 28 km in 4 hours and rows downstream a distance of 50 km in 2 hours. To row a distance of 44.8 km in still water, he will take :
2.8 hours
Let the speed of boat be x and speed of stream be y.
Abhi rows upstream a distance of 28 km in 4 h.
So, speed in upstream = 28/4 = 7 km/hr;
x - y = 7 ---(1);
Abhi rows downstream a distance of 50 km in 2 h.
So, speed in downstream = 50/2 = 25 km/hr;
x + y = 25 ---(2);
On eq (1) + (2),
2x = 32;
x = 16;
Time taken to row a distance of 44.8 km in still water = 44.8/16 = 2.8 hr
, Avg: 00:41 , 51%✓ SSC CGL 201667)X and Y are two stations which are 280 km apart. A train starts at a certain time from X and travels towards Y at 60 kmph. After 2hours, another train starts from Y and travels towards X at 20 kmph. After how many hours does the train leaving from X meet the train which left from Y?
4 hours
Distance between X and Y = 280 km
Distance covered by train starting from X in 2 hours = 2 x 60 = 120km. Remaining distance = 280 - 120 = 160km Relative speed = 60 + 20 = 80kmph Time taken to cover 160km 160/80 = 2hours Required time of meeting = 2+2 = 4hours