Time and Distance
58 solved SSC CGL Quantitative Aptitude previous year questions on Time and Distance, each with the correct answer and a full explanation.
Q1
A bus travels 150 Km in 3 hours and then travel next 2 hours at 60 Km/hr. Then the average speed of the bus will be -
✓ Correct answer: b) 54 Km/hr
ExplanationDistance covered in 2 hrs with the speed of 60 km/hr = 2 × 60 = 120 Total distance = 150 + 120 = 270 Total time = 2 + 3 = 5 hrs As we know, Average speed = Total distance/Total Time ∴ Average speed = 270/5 = 54 km/hr
Q2
A taxi going at 90 km/hr takes 35 minutes to travel a certain distance. By how much should it increase its speed (in km/hr) to travel the same distance in 21 minutes?
✓ Correct answer: a) 60
ExplanationGiven, Speed of taxi = 90 km/hr Time = 35 minutes = hour Distance = km New Time = 21 minutes = hour New speed = km/h Increasement in speed = 150 – 90 = 60 km/hr Hence, Option A is the correct answer.
Q3
A man travelled a distance of 99 km in 9 hours. He travelled partly on foot @9 km/hr and partly on bicycle @ 18 km/hr. What is distance (in kms) travelled on foot?
✓ Correct answer: c) 63
ExplanationGiven, Distance = 99 km Time = 9hr Speed on foot = 9 km/hr Speed on bicycle = 18 km/hr Let distance travelled on foot = a km Then distance travelled on bicycle = (99 – a) km According to the question, Time taken on foot + Time taken on Bicycle = 9 hr Hence, Distance travelled on foot = 63 km Hence, Option C is the correct answer.
Q4
If I walk at 7/6 of my usual speed, then I reach my office 15 minutes early. What is the usual time taken (in minutes) by me to reach the office?
✓ Correct answer: d) 105
ExplanationLet usual speed = x Total distance = y According to the question, Hence, Option D is the correct answer.
Q5
Excluding stoppages, the speed of a train is 120 kmph and including stoppages, it is 50 kmph. For how many minutes does the train stop per hour?
✓ Correct answer: c) 35
ExplanationThe speed of the train with stoppage = 50 km/h The speed of a train without stoppage = 120 km/h Difference speed = 120-50=70 km/h Stoppage time minutes Hence, Option C is the correct answer.
Q6
If a person walks at 15 km/hr instead of 9 km/hr, he would have walked 3 km more in the same time. What is the actual distance (in kms) travelled by him?
✓ Correct answer: c) 4.5
ExplanationGiven, Speed (A) = 15 km/hr Speed (B) = 9 km/hr Let, distance travelled at A speed = a km then, distance travelled at B speed = (a + 3) km According to the question, km Actual distance = Distance travelled at 9 km/hr = a = 4.5 km Hence, Option C is the correct answer.
Q7
If a boat goes a certain distance at 30 km/hr and comes back the same distance at 60 km/hr . What is the average speed (in km/hr) for the total journey?
✓ Correct answer: c) 40
ExplanationGiven, Speed (A) = 30 km/hr Speed (B) = 60 km/hr We know, for the same distance Average Speed = Hence, Option C is the correct answer.
Q8
To travel 432 km, an Express train takes 1 hour more than Duronto. If however, the speed of the Express train is increased by 50%, it takes 2 hours less than Duronto. What is the speed (in km/hr) of Duronto train?
✓ Correct answer: b) 54
ExplanationGiven, Total distance = 432 km Let, the speed of the Duronto train = a km/hr Speed of Express train = b km/hr According to question Time taken by Duronto train + 1 = Time taken by Express train …(i) Now, if the speed of the Express train increased by 50% The new speed of express train = 1.5b km/hr Time taken by Express Train + 2 = Time taken by Duronto [from eq.(i)] Hence, Speed of Duronto train = 54 km/hr Hence, Option B is the correct answer.
Q9
A bus travels 2/5 of a total journey at its usual speed. The remaining distance was covered by bus at 6/7 of its usual speed. Due to slow speed it reaches its destination 50 minutes late. If the total distance is 200 kms, then what is the usual speed (in km/hr ) of bus?
✓ Correct answer: b) 24
ExplanationGiven, Distance = 200 km Let the usual speed of the bus = 7a km/hr According to the question, Distance traveled at the usual speed = km Time taken = hours Remaining distance = 200 – 80 = 120 km Speed for remaining distance = km/h Time taken = hours Time to cover 200 km at 7a km/hr = hours Difference between time = 50 minutes = hours Usual Speed of bus = 7a = km/h Hence, Option B is the correct answer.
Q10
Two trains are moving in the opposite directions at speed of 43 km/h and 51 km/h respectively. The time taken by the slower train to cross a man sitting in the faster train is 9 seconds. What is the length (in metres) of the slower train?
✓ Correct answer: a) 235
ExplanationGiven, the speed of a slower train = 43 km/hr Speed of faster train = 51 km/hr According to the question, trains are going in the opposite direction then, Relative Speed=43 + 51=94 km/hr=94 = m/sec Now , the time taken to cross a man sitting in the faster train = 9 sec = 9 Length of slower train = 9 =235 m Hence, Option A is the correct answer.
Q11
A train of length 100 m crosses another train of length 150 m, running on a parallel track in the opposite direction in 9 seconds. If the speed of train having length 150 m is 40 km/hr, then what is the speed (in km /hr ) of the other train?
✓ Correct answer: d) 60
ExplanationThe sum of lengths of train =100+150=250m Speed = Distance/Time Speed = = 100 km/h Two trains are running in opposite directions, Relative speed = sum of their speeds 100 = 40 + Speed of other train Speed of other train = 100 - 40 = 60 km/h Hence, Option D is the correct answer.
Q12
Diameter of the wheel of a cycle is 21cm. The cyclist takes 45 minutes to reach a destination at a speed of 16.5km/hr. How many revolutions will the wheel make during the journey?
✓ Correct answer: b) 18750
ExplanationDistance traveled by the cyclist in 45 minutes = Circumference of wheel = Let, N be the number of revolution ATQ, 66×N=12.375 × 100000 N=18750 Hence, Option B is the correct answer.
Q13
A man makes four trips of equal distances. His speed on first trip was 60 km/hr and in each subsequent trip his speed was half of the previous trip. What is the average speed (in km/ hr) of the man in these four trips?
✓ Correct answer: a) 16
ExplanationGiven, Speed for 1st trip = 60 km/hr Let, the distance of each trip = 100a km Time taken = hours According to question Speed of 2nd trip = km/h Time taken = hours Speed for 3rd trip = km/h Time taken = hours Speed for 4th trip = km/h Time taken = hours Total time for all 4 trips = hours Total distance of all 4 trips = km Average Speed = km/h Hence, Option A is the correct answer.
Q14
To cover a distance of 144 km in 3.2 hours what should be the average speed of the car in meters/second?
✓ Correct answer: a) 12.5
ExplanationWe know that: Speed = Distance/Time Average speed of the car = 144/3.2 = 45 km/hr = 45×(5/18) =12.5 m/sec.Hence, Option A is the correct answer.
Q15
Walking at of his usual speed, a person reaches his office 20 minutes late than the usual time. His usual time in minutes is:
✓ Correct answer: b) 30
ExplanationLet the original speed of the person is 5x km/hr.Let he takes t minutes to reach the office if he goes at the original speed.Distance=Speed×Time=5x km/hr×t min=5x× km New speed=5x× =3x km/hr Required time to reach the office=(t+20) minutes= hr Distance=3x× km According to the question, Hence, Option B is the correct answer.
Q16
Walking at of his usual speed, a person reaches his office 10 minutes later than the usual time. His usual time in minutes is:
✓ Correct answer: a) 35
ExplanationLet the original speed of the person is 9x km/hr.Let he takes t minutes to reach the office if he goes at the original speed.Distance=Speed×Time=9x km/hr×t min=9x× km New speed=9x× =7x km/hr Required time to reach the office=(t+10) minutes= hr Distance=7x× km According to the question, Hence, Option A is the correct answer.
Q17
Walking at of his usual speed, a person reaches his office 18 minutes late than the usual time. His usual time in minutes is:
✓ Correct answer: b) 54
ExplanationLet the original speed of the person is 4x km/hr.Let he takes t minutes to reach the office if he goes at the original speed.Distance=Speed Time= New speed=4x =3x km/hr Required time to reach the office=(t+18) minutes= Distance= km According to the question, Hence, Option B is the correct answer.
Q18
A train crosses a pole in 12 , and a bridge of length 170 in 36 . Then the speed of the train is:
✓ Correct answer: c) 25.5
Explanationbridge of length = 170m A train crosses a pole = 12 Speed Let length of the train = x m Let speed of train = s m/sec Speed = s = x= 12s … (1) now, s = ...(2) from (1) and(2) = 24s = 170 s = Hence, Option C is the correct answer.
Q19
Two racers run at a speed of 100 m/min and 120 m/min, respectively. If the second racer takes 10 minutes less than the first to complete the run, then how long is the race?
✓ Correct answer: c) 6 km
ExplanationGiven, the speeds of two racers is 100 m/min and 120 m/min respectively.Ratio of their speed = 100 : 120 = 5 : 6 We know that, Time is inversely proportional to speed.So, Time ratio = 6 : 5 Suppose the time be = 6x and 5x According to the question 6x - 5x = 10 x = 10 min To complete the race, the first racer's time taken will be 6x = 6×10 = 60 min Distance = Speed × Time Distance = 60 × 100 = 6000 meter = 6 km Thus, the race distance is 6 km.Hence, the correct answer is option (C).
Q20
A private taxi company charges a fixed charge along with a per kilometer charge based on the distance covered. For a journey of 24 km, the charges paid are ₹ 368 and for a journey 32km, the charges paid are ₹464. How much will a person have to pay for travelling a distance of 15 km ?
✓ Correct answer: d) 260
ExplanationHere we have been given the charge of a taxi to cover a distance of and , that charge includes some fixed charge of taxi and some per kilometer charge based on the distance covered, in that we find the relation, how much will it pay us to cover a distance of .Given:- -For a journey of , the charges paid are Rs 368 -For a journey of , the charges paid are Rs 464 - Let the fixed charge of taxi is Let the per kilometer charge of taxi is According to question Subtracting equation 1 from equation 2 If we put the value of in equation (1), we get - For travelling a distance of a person have to pay put the value of and , we get
Q21
Akhil takes 30 minutes extra to cover a distance of 150 km if he drives 10 km/h slower than his usual speed. How much time will it take to drive 90 km if he drives 15 km per hour slower than his usual speed?
✓ Correct answer: a) 2h
ExplanationLet, the usual speed of Akhil = x km/hr Now, according to the question, x2 – 10x = 3000 x2 – 10x – 3000 = 0 x2 – 60x + 50x – 3000 = 0 x(x – 60) + 50(x – 60) = 0 (x + 50)(x - 60) = 0 x = -50, 60 Speed can’t be negative so, the usual speed of Akhil = 60 km/hr Therefore, required time taken to drive 90 km = = = 2 h Hence, Option A is the correct answer.
Q22
If a train runs with the speed of 72km/h, it reaches its destination late by 15 minutes. However, if its speed is 90 km/h, it is only 5 minutes late. The correct time to cover its journey in minutes is:
✓ Correct answer: b) 35
ExplanationIf a train runs at the speed of 72 km/h, it reaches its destination late 15 minutes.However, if its speed is 90 km/h, it is only 5 minutes late.Let, total distance = D km According to the question, Hence, Distance = 60 km If the train runs at the speed of 72 km/h, it reaches its destination late 15 minutes.Therefore, the correct time to cover its journey = Hence, Option B is the correct answer.
Q23
A train is to cover 370 km at a uniform speed. After running 100 km, the train could run at a speed 5 km/h less than its normal speed due to some technical fault. The train got delayed by 36 minutes. What is the normal speed of the train, in km/h?
✓ Correct answer: a) 50
ExplanationLet, the normal speed of the train be x km/h.Then, reduced speed = x – 5 km/h Then, time taken to cover 370 km at normal speed = hr.Actual time taken = hr.Now, as per question, Delay = 36 minutes ⇒ ⇒ ⇒ ⇒ ⇒ x2 – 5x = 2250 ⇒ x2 – 50x + 45x – 2250 = 0 ⇒ x(x – 50) + 45(x – 50) = 0 ⇒ (x – 50) (x + 45) = 0 ⇒ x – 50 = 0 or x + 45 = 0 ⇒ x = 50 or x = -45 (speed can’t be negative) ⇒ x = 50 Therefore, the normal speed of train is 50 km/h Hence, Option A is the correct answer.
Q24
Shyam drives his car 30 km at a speed of 45km/h and, for the next 1 hr 20 min , he drives it at a speed of 51 km/h. Find his average speed (in km/h ) for the entire journey.
✓ Correct answer: a) 49
ExplanationTime taken by car to cover distance of 30 km = Distance travelled by car at 51 km/hr = Speed × time = 51 × ( ) = 68 km Average Speed = Hence, the correct answer is (A).
Q25
A journey of 900 km is completed in 11 h. If two-fifth of the journey is completed at the speed of 60 km/h, at what speed (in km / h ) is the remaining journey completed?
✓ Correct answer: d) 108
ExplanationDistance covered at a speed of 60 km/h = = 360 km Time required to cover 360 km = = 6 hours Remaining distance = 900 – 360 = 540 km Required speed = = 108 km/h Hence, the correct answer is (D).
Q26
The ratio of the speeds of two trains is 2 :7. If the first train runs 250 km in 5 hours, then the sum of the speeds (in km h) of both the trains is:
✓ Correct answer: d) 225
ExplanationSpeed of the first train = = 50 km/h The sum of the speeds of both the trains = 50 × = 225 km/h.Hence, the correct answer is (D).
Q27
The distance between two towns is covered in 7 hours at a speed of 50 km/h. By how much should the speed (in km/h) be increased so that 2 hours of travelling time will be saved?
✓ Correct answer: b) 20
ExplanationDistance = 7 × 50 = 350 km Required speed = = = 70 km/h Required increase in speed = 70 – 50 = 20 km/h Hence, the correct answer is (B).
Q28
A 240-m long train crosses a 360-m long tunnel in 30 seconds. What is the speed of the train (in km/h)?
✓ Correct answer: a) 72
ExplanationTime required by a train to cross a tunnel = Let, the speed of the train be v m/s.Then, = 30 ⇒ v = = 20 Speed of train = 20 m/s = 20 × = 72 km/h Hence, the correct answer is (A).
Q29
Vinay and Mahesh are 250 metres apart from each other. They are moving towards each other with the speed of 36 and hr respectively. In how much time will they meet each other?
✓ Correct answer: c) 10 seconds
ExplanationDistance between Vinay and Mahesh = 250 m Relative speed of Vinay and Mahesh = 36 + 54 = 90 km/hr = Time = Hence, 10 is the correct answer.
Q30
A railway engine crosses two bridges 400 m and 235 m long in 100 seconds and 60 seconds respectively. Twice the length of the engine (in metres) is:
✓ Correct answer: b) 25
ExplanationLet, the length of the railway engine be x metre.Since the speed of in both the cases are equal, and, Speed = Therefore, = ⇒ 60x + 24000 = 100x + 23500 ⇒ 40x = 500 ⇒ x = 12.5 Twice the length of railway engine = 12.5 × 2 = 25 m Hence, Option B is the correct answer.
Q31
A train of length 287 m, running at 80 km/h, crosses another train moving in the opposite direction at 37 km/h in 18 seconds. What is the length of the other train?
✓ Correct answer: b) 298 m
ExplanationRelative speed = 80 + 37 = 117 km/h = 117 × = 32.5 m/s.Relative distance = Relative speed × Time = 32.5 × 18 = 585 m Hence, Length of second train = Relative distance – Length of first train = 585 – 287 = 298 m
Q32
If Raman drives his bike at a speed of 24 km/h , he reaches his office 5 minutes late. If he drives at a speed of 30 km /h , he reaches his office 4 minutes early. How much time (in minutes) will he take to reach his office at a speed of 27 km/h?
✓ Correct answer: c) 40
ExplanationLet the distance between his office and his home be “d” km d = 18 km time taken at speed 27 km/hr = Hence, the correct answer is (C).
Q33
A truck runs 492 km on 36 Litter of diesel. How many kilometres can it run on 33 Litter of diesel?
✓ Correct answer: c) 451 km
ExplanationAccording to the given data : In 36 Liters of diesel, truck runs = 492 km In 33 liters of diesel, truck runs Hence required distance is = 451 km.
Q34
A river 6 m deep and 35 m wide is flowing at the rate of 2.5km/h, the amount of water that runs into the sea per minute is:
✓ Correct answer: d) 8750 m3
ExplanationA river 6 m deep and 35 m wide is flowing at the rate of 2.5 km/h.Amount of water that runs into the sea per minute = Hence, the correct answer is (D).
Q35
Two trains are running on parallel tracks in the same direction at the speed of 80 km/h and 90 km/h, respectively. The faster train crossed the slower train in 3 minutes. If the length of one train is 230 m, then what is the length (in m) of the other train?
✓ Correct answer: a) 270
ExplanationRelative speed of trains in same direction = (90 – 80)=10 km/hr Length of both trains = time × relative Speed = Length of other train = 500 – 230 = 270 m Hence, the correct answer is (A).
Q36
In a 1500 m race, Anil beats Bakul by 150 m and in the same race Bakul beats Charles by 75 m. By what distance does Anil beat Charles?
✓ Correct answer: a) 217.50 m
ExplanationGiven that, In a 1500-metre race, Anil beats Bakul by 150 metres and Bakul beats Charles by 75 metres.Distance covered by Anil = 1500 metres Distance covered by Bakul = (1500 - 150) metres = 1350 metres Again, when Bakul runs 1500 metres, Charles runs 1500 - 75 = 1425 metres.Now, Anil beats Charles by (1500 - 1282.5) m = 217.5 m Hence, the correct answer is (A).
Q37
If Ram covers a certain journey at 60% of his usual speed, he reaches the destination late by 36 min. His usual time (in min) to reach the destination is:
✓ Correct answer: d) 54
ExplanationAccording to the given data , His usual time to reach the destination is 54 minutes.Hence, option D is the correct answer.
Q38
Two runners, Sony and Mony, start running on a circular track of length 200 m at speeds of 18 and 24 km/h, respectively, in the same direction. After how much time from the start will they meet again at the starting point?
✓ Correct answer: a) 120 sec
ExplanationLength of circular track = 200 m Speed of Sony = 18 km/h Speed of Mony = 24 km/h Difference between their speed = 6 km/h Time taken to cover 200 m at m/s sec.So, they will meet again after 120 seconds.Hence the correct option is A.
Q39
A policeman follows a thief who is 600m ahead of the policeman. If the policeman and the thief run at speeds of 10 kmph and 8 kmph respectively, in how much time (in minutes), will the policeman catch the thief ?
✓ Correct answer: c) 18
ExplanationGiven, Speed of police is 10 km/hrs and speed of thief is 8 km/hrs So, their relative speed = (10-8) km/hrs =2 km/ hrs = m/sec and distance between them is 600 m. Time taken to caught = 600 = 1080 seconds= 18 minutes.Hence, the correct answer is (C).
Q40
A goods train 350 m long passes through a tunnel of length 1250 m in 80 seconds. What is the speed of the train?
✓ Correct answer: d) 72 km/h
ExplanationTotal distance covered by the train = Length of train + Length of tunnel 350 m + 1250 m = 1600 m Time taken to cover this distance = 80 seconds To find the speed of the train, we can use the formula: Speed = Distance/Time Speed = m/s We need to convert this speed from m/s to km/h, as the options are given in km/h.1 m/s 3.6 km/h km/hr Hence, Option D is the correct answer.
Q41
A constable Ram is 225 m behind a thief Somesh. Ram runs 50 m and Somesh runs 30 m in a minute. After how much time will the constable Ram catch the thief Somesh?
✓ Correct answer: c) 11 minutes 15 seconds
ExplanationAccording to question, Speed of police is 50 m/min and speed of thief is 30 m/min So, relative speed of police is 20 m/min, and gap between them is 225 meter So, the time teken by police to catch the thief = = 11 min 15 second Hence, the correct option is C.
Q42
Racer and racer run a race of on a circular track of length . Both complete one round in and , respectively. After how much time from the start will the faster person meet the slower person for the last time?
✓ Correct answer: b) 4000 sec
ExplanationGiven, total distance = 18 km = 18000 meter, length of the track = 800 meter speed of A = and speed of B = Now, L.C.M. of 200 sec and 250 sec is 1000 sec and the total time taken by A to complete the race is Hence, they meet 1st time after 1000 sec 2nd time after 2000 sec, 3rd time after 3000 sec, and 4th and the last time after 4000 sec.Hence, the correct option is B.
Q43
Two trains and of lengths and , respectively, are running in the same direction on parallel tracks at and , respectively. How much time will the trains take to cross each other completely?
✓ Correct answer: a) 86 seconds
ExplanationIt is given that, Two trains P and Q of lengths 320 m and 540m respectively, are running in the same direction on parallel tracks at 108 km/h and 144 km/h.Relative speed of train = 144 - 108 = 36 km/h = 10 m/sec Total length of both train = 320 + 540 = 860 m Now, time taken by train to cross each-other = = 86 second.Hence, the correct option is A.
Q44
Anand covers a certain distance in the first lag of 5 hours at the speed of 50 km/h. In the second lag, he increased the speed by 20% due to which he covered 20% extra distance than that of the first lag. He covered the third lag at the average speed of the first two lags and covered extra distance than that of the second lag distance. How much total time (in hours) did he take to complete all three lags?
✓ Correct answer: a) 16
ExplanationFirst Lag: Speed= 50 km/h Time= 5 hours Distance = Speed × Time = 50 km/h × 5 h = 250 km Second Lag: Speed Increase=20% Increased Speed= 50+50 20% = 60 km/h Distance Covered=20% extra distance of the distance covered in the first lag =250+250 20%=300km Time = = 5 hours Third Lag: Speed= = 55 km/h Distance Covered=10% extra distance of the distance covered in the second lag =300+300 10%=330 km Time = = 6 hours The total time taken to complete all three legs = 5+5+6=16 hours Hence, the correct answer is (A).
Q45
In a circular path of 600 m, Pankaj and Rohit start walking in opposite directions from the same point at the speeds of 2.85 m/s and 5.4 km/h respectively. After how many minutes will they meet for the first time? (Rounded off to one decimal point)
✓ Correct answer: b) 2.3
ExplanationIn a circular path of 600 m, Pankaj and Rohit start walking in opposite directions from the same point at the speeds of 2.85 m/s and 5.4 km/h respectively.Speed of Rohit = 5.4 = 1.5 m/s Relative speed of Pankaj and Rohit = 2.85 + 1.5 = 4.35 m/s They meet for the first time after = 600 ÷ 4.35 = 137.93 seconds = 137.93 ÷ 60 = 2.3 minutes Hence, the correct option is B.
Q46
Vipin travels one-third of the distance of a journey at a speed of 30 km/h and the remaining distance at a speed of 40 km/h. If he took a total of 12 hours to complete the journey, what was the total distance (in km) of the journey?
✓ Correct answer: a) 432
ExplanationLet the total distance be D km.Distance1= (D/3)/30 (one-third of the total distance) Distance 2= (2D/3)/3 (remaining distance) Time taken for Distance 1 = (D/3)/30 Time taken for Distance 2 = (2D/3)/40 Total Time = Time for Distance1 + Time for Distance2 Hence, Option A is the correct answer.
Q47
A policeman chasing a thief is behind the thief. The speed of thief is of the speed of the policeman and policeman catches him in 12 minutes. What is the speed of the thief (in ?
✓ Correct answer: a) 10
ExplanationGiven that, distance between the policeman and the thief is 0.5 km.The speed of thief is 80% of the speed of the policeman.Let, the speed of the policeman is km/hr.Speed of the thief = km/hr Relative speed = km/hr Policeman catches the thief in 12 minutes i.e hr.According to the question, Hence, Speed of the thief = =4 2.5=10 km/hr Hence, the correct answer is (A).
Q48
A train traveling at 70 km/h crosses another train traveling in the same direction at 34 km/h in 25 seconds. What is the combined length of both the trains (in metres)?
✓ Correct answer: b) 250
ExplanationSpeed of first train is 70 km/hrs and speed of second train is 34 km / hrs Since they are travelling in the same direction then Relative speed of train = 70 - 34 = 36 km/hrs = 10 m/sec and time taken to cross the train is = 25 sec The combined length of both train = 25 × 10 = 250 meter Hence, the correct option is B.
Q49
A thief steals an item and escapes, running at 20 km/h. A policeman arrives at the spot of the crime after 6 minutes and immediately starts chasing the thief. 24 minutes after the policeman started to chase the thief, there is still a gap of 400 m between the two. At what distance from the spot of crime would the policeman catch up with the thief, and what is the speed at which the policeman ran?
✓ Correct answer: d) 12 km; 24 km/h
ExplanationLet the speed of a policeman = s km/hr Distance covered by thief in 30 minutes = km Distance covered by policeman in 24 minutes = According to the given question, 10 = Relative speed = 24 - 20 = 4 km/hr m/s Time taken to cover 400 m at relative speed sec. = 6 min So, the policeman will catch the thief 6 + 24 + 6 = 36 min after the crime.Distance covered by the thief in 36 min = km.Hence, the correct option is D.
Q50
In linear race, beats by 120 metres or . What is the time taken by to cover the race?
✓ Correct answer: a) 220 sec
ExplanationWe have, Track length = 1 km = 1000 m We know that, Distance = Speed × Time "A" beats "B" by 120 m or 30 sec, means "B" covers 120 m in 30 sec Speed of "B" = = 4 m/s Time to cover 1000 m by B = sec "A" beats "B" by 30 sec means "A" reach 30 sec early Time taken by "A" to complete the race = 250 – 30 = 220 sec Hence, the correct answer is (A).
Q51
As part of his journey, a person travels 120 km at 80 km/h, the next 100 km at 40 km/h,and comes back to the starting point at 75 km/h. The average speed of the person throughout the journey (approximately) is:
✓ Correct answer: a) 63.46 km/h
ExplanationTotal distance covered = 120+100+220= 440Km Time taken to cover 120km by speed 80km/hr = 120/80 = 3/2hrs Time taken to cover 100km by speed 40km/hr = 100/40 = 5/2hrs Time taken to cover 220km by speed 75m/hr = 220/75 = 44/15hrs Total time taken to cover 440km = = Therefore, Average Speed = = 63.46 km/hr Hence, option A is the correct answer.
Q52
A thief steals an item and escapes, running at a speed of 15 km/h. A policeman arrives at the spot of the crime after 4 minutes and immediately starts chasing the thief. 16 minutes after the policeman started to chase the thief; there is still a gap of 200 m between the two. At what distance from the spot of the crime will the policeman catch up the thief and what is the speed (in km/h) of the policeman?
✓ Correct answer: b) 6 km; 18
ExplanationSpeed of thief = 15km/h = m/s = m/s | | SSC Police came after 4 min and immediately start chasing the thief for 16 min so, for 20 min thief was running continuously Distance travelled by thief in 20 min or 1200 sec = m but, it is given that after 20 min there was still a gap of 200m between the police and thief and 4800m wass covered by police in 16min or 960 sec, because it is given that there was a gap of 200m after 20min of travel by thief so speed of police = m/s = km/h now, effective/ relative speed between the thief and police would be = 18 - 15 = 3km/h = m/s now to cover 200m distance, time = s In 240 sec distance travelled by thief = m = 1km Hence, total distance covered by thief = 6km and speed of police =18km/h Hence, Option B is correct
Q53
Jehangir had to cover a distance of 90 km in an hour. During the first 25 minutes he travelled at a speed of 15.2 metres per second. How many metres did Jehangir cover per second during the remaining period to reach his destination just on time?
✓ Correct answer: c) 32
ExplanationTotal distance = 90 km and time = 1 hour = 60 minutes = 3600 second In the first 25 minutes the distance covered by him = 25 × 60 × 15.2 = 22800 meter Remaining distance = 90000 - 22800 = 67200 meter So the distance covered by him per second = Hence, the correct option is C.
Q54
A policeman saw a thief at a distance of 400 m. The thief started running at a speed of 10 km/h and the policeman chased him at a speed of 12 km/h in the same direction. At what distance from the starting point will the policeman catch the thief ?
✓ Correct answer: a) 2.4 km
ExplanationRelative speed = 12 - 10 = 2 km/hr = m/s Time taken by policeman to catch a thief sec = hours Distance covered by a policeman to catch a thief = 12 = 2.4 km Hence, the correct option is A.
Q55
In a circular race of 4225 m , X and Y start from the same point and at the same time at speeds of 54 km/h and 63 km/h When will they meet again for the first time on the track when they are running in the opposite direction?
✓ Correct answer: c) 130 seconds
ExplanationConverting speeds to m/s: Speed of X = = 15 m/s Speed of Y = = 17.5 m/s Relative speed = 15 m/s + 17.5 m/s = 32.5 m/s Now, we can use the formula: Time = Time = = 130 seconds Therefore, X and Y will meet again for the first time on the track when they are running in the opposite direction after approximately 130 seconds.Hence, Option C is correct
Q56
A train 900m long is running at 108 km/h. How long will it take to clear a 900 m long platform completely?
✓ Correct answer: a) 60 s
ExplanationLength of a train = 900 m Length of a platform = 900 m Speed of a train = 108 km/hr= Total time taken by train to clear a platform = = 60 s Hence, the correct answer is (A).
Q57
Reshma covers 45 km at a speed of 15 km/h by bicycle, 80 km at a speed of 40 km/h by car, and another 6 km at a speed of 2 km/h on foot. Find her average speed for the whole journey (correct to 2 decimal places).
✓ Correct answer: a) 16.38 km/h
ExplanationWe know that, Time taken = Distance /Speed Average speed= Total Distance/ Total time taken Resham's time taken to cover 45 km by bicycle= hr Resham's time taken to cover 40 km by car= hr Resham's time taken to cover 6 km on foot= hr ∴ The average speed= Hence, Option A is the correct answer.
Q58
A cyclist rides in 120 minutes and rides another in 150 minutes. What is the average speed of the cyclist, in ?
✓ Correct answer: c) 10
ExplanationWe have, D1 = 20 km, t1 = 120min = 2h D2 = 25 km, t2 = 150min = 2.5h We know that, Average speed = Average speed for the entire journey, = 10 hours Hence, option C is correct
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