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### Question:
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? | ### Answer:
Speed = 60 x5/18m/sec=50/3m/sec.
Length of the train = (Speed x Time).
Length of the train =50/3x 9 m = 150 m. |
###Question:
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: | ###Answer:
Speed of the train relative to man =125/10m/sec
=25/2m/sec.
=25/2x18/5km/hr
= 45 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 x = 50 km/hr.
|
###Question:
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: | ###Answer:
Speed = 45 x5/18m/sec = 25/2m/sec.
Time = 30 sec.
Let the length of bridge be x metres.
Then, 130 + x/30=25/2
2(130 + x) = 750
x = 245 m. |
###Question:
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is: | ###Answer:
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.
27x + 17y/x+ y= 23
27x + 17y = 23x + 23y
4x = 6y
x/y=3/2 |
###Question:
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? | ###Answer:
Speed = 54 x5/18m/sec = 15 m/sec.
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then, x + 300/36= 15
x + 300 = 540
x = 240 m. |
###Question:
A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long? | ###Answer:
Speed = 240/24m/sec = 10 m/sec.
Required time =240 + 650/10sec =89 sec. |
###Question:
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is: | ###Answer:
Let the length of each train be x metres.
Then, distance covered = 2x metres.
Relative speed = (46 - 36) km/hr
=10 x5/18m/sec
=25/9m/sec
2x/36=25/9
2x = 100
x = 50. |
###Question:
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? | ###Answer:
Formula for converting from km/hr to m/s:X km/hr =X x5/18m/s.
Therefore, Speed =45 x 5/18 m/sec=25/2 m/sec.
Total distance to be covered = (360 + 140) m = 500 m.
Formula for finding Time =Distance/Speed
Required time =500 x 2/25sec= 40 sec. |
###Question:
Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is: | ###Answer:
Relative speed = (60+ 90) km/hr
=150 x5/18 m/sec
=125/3 m/sec.
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
Required time = (2000 x 3/125)sec = 48 sec. |
###Question:
A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger? | ###Answer:
Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr
=36 x5/18m/sec
= 10 m/sec
Distance to be covered = (240 + 120) m = 360 m
Time taken =360/10sec = 36 sec |
###Question:
A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? | ###Answer:
Relative speed = (120 + 80) km/hr
=200 x5/18m/sec
=500 /9 m/sec.
Let the length of the other train be x metres.
Then, x + 270/9=500/9
x + 270 = 500
x = 230. |
###Question:
A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train? | ###Answer:
Speed = 72 x5/18 m/sec= 20 m/sec.
Time = 26 sec.
Let the length of the train be x metres.
Then, x + 250/26= 20
x + 250 = 520
x = 270. |
###Question:
Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is: | ###Answer:
Let the speed of the slower train be x m/sec.
Then, speed of the faster train = 2x m/sec.
Relative speed = (x + 2x) m/sec = 3x m/sec.
(100 + 100)/8= 3x
24x = 200
x =25/3
So, speed of the faster train = 50/3m/sec
=50/3 x18/5 km/hr
= 60 km/hr. |
###Question:
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is: | ###Answer:
Relative speed = (60 + 40) km/hr =100 x 5/18 m/sec= 250/9 m/sec.
Distance covered in crossing each other = (140 + 160) m = 300 m.
Required time = 300 x 9/250sec = 54/5 sec = 10.8 sec. |
###Question:
A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? | ###Answer:
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.
=66 x5/18 m/sec
=55/3 m/sec.
Time taken to pass the man =110 x3/55 sec = 6 sec. |
###Question:
A train travelling at a speed of 75 mph enters a tunnel 31/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges? | ###Answer:
Total distance covered
=(7/2+1/4)miles
=15/4 miles.
Therefore Time taken
=(15/4 x 75)hrs
=1/20 hrs
=(1/20 x 60) min.
= 3 min |
###Question:
A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is: | ###Answer:
Speed = (78 x5/18)m/sec =(65/3) m/sec.
Time = 1 minute = 60 seconds.
Let the length of the tunnel be x metres.
Then, (800 + x/60) =65/3
=> 3(800 + x) = 3900
=> x = 500. |
###Question:
A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? | ###Answer:
Speed = (300/18 )m/sec =50/3m/sec.
Let the length of the platform be x metres.
Then, (x + 300)/39=50/3
=> 3(x + 300) = 1950
=> x = 350 m. |
###Question:
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is: | ###Answer:
Let the length of the train be x metres and its speed by y m/sec.
Then, x/y= 15 => y =x/15 .
Therefore (x + 100)/25=x/15
=> 15(x + 100) = 25x
=> 15x + 1500 = 25x
=> 1500 = 10x
=> x = 150 m |
###Question:
A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train? | ###Answer:
Let the length of the train be x metres and its speed by y m/sec.
Then, x/y = 8 => x = 8y
Now, (x + 264)/20= y
=> 8y + 264 = 20y
=> y = 22
Therefore Speed = 22 m/sec =(22 x18/5)km/hr = 79.2 km/hr |
###Question:
How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? | ###Answer:
Speed of the train relative to man= (63 - 3) km/hr
= 60 km/hr
=(60 x 5/18) m/sec
=(50/3) m/sec.
Therefore Time taken to pass the man
=(500 x 3/50) sec
= 30 sec |
###Question:
Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one. |
###Answer:
Relative speed = (45 + 30) km/hr
= (75 x5/18) m/sec
= (125/6)m/sec.
We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.
So, distance covered = Length of the slower train.
Therefore, Distance covered = 500 m.
Therefore Required time =(500 x 6/... |
###Question:
Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is | ###Answer:
Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12
=> 2x = 20
=> x = 10.
Therefore Speed of each train = 10 m/sec = (10 x18/5)km/hr = 36 km/hr. |
###Question:
Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction? | ###Answer:
Speed of the first train =(120/10)m/sec = 12 m/sec.
Speed of the second train =(120/15)m/sec = 8 m/sec.
Relative speed = (12 + 8) = 20 m/sec.
Therefore Required time =[(120 + 120)/20]sec = 12 sec. |
###Question:
A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is: | ###Answer:
Let the speed of the second train be x km/hr.
Relative speed = (x + 50) km/hr
=[(x + 50) x5/18]m/sec
=[(250 + 5x)/18]m/sec.
Distance covered = (108 + 112) = 220 m.
Therefore 220/((250 + 5x)/18)= 6
=> 250 + 5x = 660
=> x = 82 km/hr. |
###Question:
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train? | ###Answer:
Relative speed = (40 - 20) km/hr =(20 x 5/18)m/sec =(50/9)m/sec.
Therefore Length of faster train =(50/9 x 5)m =250/9m |
###Question:
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: | ###Answer:
2 kmph =(2 x5/18)m/sec =5/9m/sec.
4 kmph =(4 x5/18) m/sec = 10/9 m/sec.
Let the length of the train be x metres and its speed by y m/sec.
Then, x/(y - 5/9)= 9 and(x/(y -10/9))= 10.
Therefore 9y - 5 = x and 10(9y - 10) = 9x
=> 9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50.
Therefore Length of t... |
###Question:
A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? | ###Answer:
4.5 km/hr =(4.5 x5/18)m/sec =5/4 m/sec = 1.25 m/sec, and
5.4 km/hr =(5.4 x5/18) m/sec = 3/2 m/sec = 1.5 m/sec.
Let the speed of the train be x m/sec.
Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5
=> 8.4x - 10.5 = 8.5x - 12.75
=> 0.1x = 2.25
=> x = 22.5
Therefore Speed of the train = (22.5 x 18/5)km/hr = 81 km/hr... |
###Question:
A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is | ###Answer:
Let the length of the first train be x metres.
Then, the length of the second train is (x/2)metres.
Relative speed = (48 + 42) kmph =(90 x 5/18)m/sec = 25 m/sec.
Therefore [x + (x/2)]/25 = 12 or3x/2 = 300 or x = 200.
Therefore Length of first train = 200 m.
Let the length of platform be y metres.
Speed of t... |
###Question:
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? | ###Answer:
Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
=> 45x = 135
=> x = 3.
So, they meet at 10 a.m. |
###Question:
Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is: | ###Answer:
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √ b : √ a = √ 16 : √ 9 = 4 : 3 |
###Question:
A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? | ###Answer:
Speed = 600/5 x 60m/sec.
= 2 m/sec.
Converting m/sec to km/hr (see important formulas section)
=(2 x18/5)km/hr
= 7.2 km/hr |
###Question:
An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1(2/3) hours, it must travel at a speed of: | ###Answer:
Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1(2/3) hours as 5/3 hours]
Required speed =1200 x 3/5km/hr= 720 km/hr. |
###Question:
If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is: | ###Answer:
Let the actual distance travelled be x km.
Then, x/10=(x + 20)/14
14x = 10x + 200
4x = 200
x = 50 km. |
###Question:
A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is: | ###Answer:
Let speed of the car be x kmph.
Then, speed of the train =150/100x=(3/2)xkmph.
75/x-75/(3/2)x =125/(10 x 60)
75/x-50/x=5/24
x =(25 x24)/5 = 120 kmph. |
###Question:
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour? | ###Answer:
Due to stoppages, it covers 9 km less.
Time taken to cover 9 km =(9/54)x 60min = 10 min. |
###Question:
In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is: | ###Answer:
Let the duration of the flight be x hours.
Then, 600/x-600/(x + (1/2))= 200
600/x-1200/(2x + 1)= 200
x(2x + 1) = 3
2x^2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr |
###Question:
A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km. | ###Answer:
((1/2)x)/21+((1/2)x)/24 = 10
x/21+x/24= 20
15x = 168 x 20
x = (168 x 20)/15= 224 km. |
###Question:
The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is: | ###Answer:
Let the speed of two trains be 7x and 8x km/hr.
Then, 8x =400/4= 100
x =100/8= 12.5
Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr |
###Question:
A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is: | ###Answer:
Total time taken =160/64+160/80 hrs =9/2hrs.
Average speed = (320 x 2/9 )km/hr = 71.11 km/hr. |
###Question:
A car travelling with 5/7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car. | ###Answer:
Time taken = 1 hr 40 min 48 sec = 1 hr 40(4/5) min = 1 (51/75) hrs = 126/75 hrs.
Let the actual speed be x km/hr.
Then, 5/7x x 126/75 = 42
x =(42 x 7 x 75)/(5 x 126)= 35 km/hr. |
###Question:
In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is: | ###Answer:
Let Abhay's speed be x km/hr.
Then, 30/x-30/2x= 3
6x = 30
x = 5 km/hr |
###Question:
Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.? | ###Answer:
Let the distance travelled by x km.
Then, x/10-x/15= 2
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr =(60/10)hrs= 6 hrs.
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed =60/5kmph= 12 kmph. |
###Question:
A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is: |
###Answer:
Let the distance travelled on foot be x km.
Then, distance travelled on bicycle = (61 -x) km.
So,x/4+(61 -x)/9= 9
9x + 4(61 -x) = 9 x 36
5x = 80
x = 16 km |
###Question:
A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is : | ###Answer:
A's 1 day's work =1/15;
B's 1 day's work = 1/20
(A + B)'s 1 day's work =(1/15+1/20)=7/60
(A + B)'s 4 day's work =(7/60x 4)=7/15 .
Therefore, Remaining work =(1 -7/15)=8/15 |
###Question:
A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in: | ###Answer:
(A + B + C)'s 1 day's work =1/4
A's 1 day's work =1/16
B's 1 day's work =1/12
Therefore C's 1 day's work = 1/4-(1/16+1/12)=(1/4-7/48)=5/48
So, C alone can do the work in 48/5 days. |
###Question:
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? | ###Answer:
A's 2 day's work =1/20x 2=1/10
(A + B + C)'s 1 day's work =1/20+1/30+1/60=6/60=1/10
Work done in 3 days =1/10+1/10=1/5
Now, 1/5 work is done in 3 days
Whole work will be done in (3 x 5) = 15 days. |
###Question:
A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in: | ###Answer:
Ratio of times taken by A and B = 1 : 3.
The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.
If difference of time is 2 days, B takes 3 days.
If difference of time is 60 days, B takes(3/2x 60)= 90 days.
So, A takes 30 days to do the work.
A's 1 day's work = 1/30
B's 1 day's work... |
###Question:
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C? | ###Answer:
C's 1 day's work =1/3 - (1/6+1/8) = 1/3 -7/24=1/24
A's wages : B's wages : C's wages =1/6:1/8:1/24= 4 : 3 : 1.
C's share (for 3 days) = Rs. (3 x 1/24 x 3200) = Rs. 400. |
###Question:
If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be: | ###Answer:
Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.
Then, 6x + 8y = 1/10 and 26x + 48y = 1/2 .
Solving these two equations, we get : x =1/100 and y = 1/200 .
(15 men + 20 boy)'s 1 day's work =15/100+20/200 =1/4
15 men and 20 boys can do the work in 4 days |
###Question:
A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it? | ###Answer:
A's 1 hour's work = 1/4
(B + C)'s 1 hour's work = 1/3
(A + C)'s 1 hour's work = 1/2
(A + B + C)'s 1 hour's work =(1/4+1/3)=7/12
B's 1 hour's work =(7/12 - 1/2) =1/12
Therefore B alone will take 12 hours to do the work. |
###Question:
A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in: | ###Answer:
(A + B)'s 1 day's work =1/10
C's 1 day's work =1/50
(A + B + C)'s 1 day's work = 1/10 + 1/50 = 6/50 = 3/25
A's 1 day's work = (B + C)'s 1 day's work
From (i) and (ii), we get: 2 x (A's 1 day's work) =3/25
A's 1 day's work = 3/50
B's 1 day's work (1/10-3/50) =2/50=1/25
So, B alone could do the work... |
###Question:
A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work? | ###Answer:
Whole work is done by A in (20 x 5/4) = 25 days.
Now, (1 - 4/5)i.e., 1/5 work is done by A and B in 3 days.
Whole work will be done by A and B in (3 x 5) = 15 days.
A's 1 day's work = 1/25, (A + B)'s 1 day's work = 1/15
Therefore B's 1 day's work = (1/15 - 1/25) = 4/150 =2/75
So, B alone would do t... |
###Question:
A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the... | ###Answer:
(P + Q + R)'s 1 hour's work = ( 1/8 + 1/10 + 1/12 ) = 37/120
Work done by P, Q and R in 2 hours =(37/120 x 2)=37/60
Remaining work =(1 -37/60)=23/60
(Q + R)'s 1 hour's work =(1/10 +1/12) =11/60
Now, 11/60 work is done by Q and R in 1 hour.
So, 23/60 work will be done by Q and R in (60/11x23/60)=2... |
###Question:
A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work? | ###Answer:
B's 10 day's work =(1/15x 10)=2/3
Remaining work =( 1 - 2/3)=1/3
Now, 1/18 work is done by A in 1 day.
Therefore 1/3 work is done by A in(18 x1/3)= 6 days. |
###Question:
4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it? | ###Answer:
Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.
Then, 4x + 6y = 1/8 and 3x + 7y = 1/10
Solving the two equations, we get: x = 11/400 , y = 1/400
1 woman's 1 day's work = 1/400
10 women's 1 day's work =1/400 x 10=1/40
Hence, 10 women will complete the work in 40 days. |
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